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Journal articles on the topic 'P-adic group'

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Published: 9 March 2023
Last updated: 10 March 2023

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1

Roggenkamp, Klaus, and Leonard Scott. "Isomorphisms of p-adic Group Rings." Annals of Mathematics 126, no. 3 (November 1987): 593. http://dx.doi.org/10.2307/1971362.

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2

KOCH, ALAN, and AUDREY MALAGON. "p-ADIC ORDER BOUNDED GROUP VALUATIONS ON ABELIAN GROUPS." Glasgow Mathematical Journal 49, no. 2 (May 2007): 269–79. http://dx.doi.org/10.1017/s0017089507003680.

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AbstractFor a fixed integer e and prime p we construct the p-adic order bounded group valuations for a given abelian group G. These valuations give Hopf orders inside the group ring KG where K is an extension of $\mathbb{Q} _{p}$ with ramification index e. The orders are given explicitly when G is a p-group of order p or p2. An example is given when G is not abelian.
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3

Külshammer, Burkhard. "Central idempotents in p-adic group rings." Journal of the Australian Mathematical Society. Series A. Pure Mathematics and Statistics 56, no. 2 (April 1994): 278–89. http://dx.doi.org/10.1017/s1446788700034881.

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4

Eisele, Florian. "The p -adic group ring ofSL2(pf)." Journal of Algebra 410 (July 2014): 421–59. http://dx.doi.org/10.1016/j.jalgebra.2014.01.036.

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5

Zelenov, E. I. "p-adic Heisenberg group and Maslov index." Communications in Mathematical Physics 155, no. 3 (August 1993): 489–502. http://dx.doi.org/10.1007/bf02096724.

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6

Oliver, Robert. "Central units in p-adic group rings." K-Theory 1, no. 5 (September 1987): 507–13. http://dx.doi.org/10.1007/bf00536982.

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7

Gras, Georges. "The p-adic Kummer–Leopoldt constant: Normalized p-adic regulator." International Journal of Number Theory 14, no. 02 (February 8, 2018): 329–37. http://dx.doi.org/10.1142/s1793042118500203.

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The [Formula: see text]-adic Kummer–Leopoldt constant [Formula: see text] of a number field [Formula: see text] is (assuming the Leopoldt conjecture) the least integer [Formula: see text] such that for all [Formula: see text], any global unit of [Formula: see text], which is locally a [Formula: see text]th power at the [Formula: see text]-places, is necessarily the [Formula: see text]th power of a global unit of [Formula: see text]. This constant has been computed by Assim and Nguyen Quang Do using Iwasawa’s techniques, after intricate studies and calculations by many authors. We give an elementary [Formula: see text]-adic proof and an improvement of these results, then a class field theory interpretation of [Formula: see text]. We give some applications (including generalizations of Kummer’s lemma on regular [Formula: see text]th cyclotomic fields) and a natural definition of the normalized [Formula: see text]-adic regulator for any [Formula: see text] and any [Formula: see text]. This is done without analytical computations, using only class field theory and especially the properties of the so-called [Formula: see text]-torsion group [Formula: see text] of Abelian [Formula: see text]-ramification theory over [Formula: see text].
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8

LEE, Joongul. "Contracted Ideals of $p$-adic Integral Group Rings." Tokyo Journal of Mathematics 43, no. 2 (December 2020): 529–36. http://dx.doi.org/10.3836/tjm/1502179313.

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9

Yu, Kunrui. "p-adic logarithmic forms and group varieties II." Acta Arithmetica 89, no. 4 (1999): 337–78. http://dx.doi.org/10.4064/aa-89-4-337-378.

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10

Hare, Kathryn E., and Maziar Shirvani. "The Semisimplicity Problem for p-Adic Group Algebras." Proceedings of the American Mathematical Society 108, no. 3 (March 1990): 653. http://dx.doi.org/10.2307/2047785.

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11

Bump, Daniel, Solomon Friedberg, and Jeffrey Hoffstein. "$p$ -adic Whittaker functions on the metaplectic group." Duke Mathematical Journal 63, no. 2 (July 1991): 379–97. http://dx.doi.org/10.1215/s0012-7094-91-06316-7.

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12

Farkov, Yuri A. "Periodic wavelets on the p-adic Vilenkin group." P-Adic Numbers, Ultrametric Analysis, and Applications 3, no. 4 (November 19, 2011): 281–87. http://dx.doi.org/10.1134/s2070046611040030.

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13

Hare, Kathryn E., and Maziar Shirvani. "The semisimplicity problem for $p$-adic group algebras." Proceedings of the American Mathematical Society 108, no. 3 (March 1, 1990): 653. http://dx.doi.org/10.1090/s0002-9939-1990-0998736-0.

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14

YU, KUNRUI. "P-adic logarithmic forms and group varieties I." Journal für die reine und angewandte Mathematik (Crelles Journal) 1998, no. 502 (September 15, 1998): 29–92. http://dx.doi.org/10.1515/crll.1998.090.

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15

Dat, J. F. "On the K0 of a p-adic group." Inventiones mathematicae 140, no. 1 (April 2000): 171–226. http://dx.doi.org/10.1007/s002220050360.

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16

DANIŞMAN, Yusuf. "Regular poles for the p-adic group $GSp_4$." TURKISH JOURNAL OF MATHEMATICS 38 (2014): 587–613. http://dx.doi.org/10.3906/mat-1306-28.

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17

Soundararajan, T. "The topological group of the $p$-adic integers." Publicationes Mathematicae Debrecen 16, no. 1-4 (July 1, 2022): 75–78. http://dx.doi.org/10.5486/pmd.1969.16.1-4.10.

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18

Garaialde Ocaña, Oihana. "Cohomology of uniserial p -adic space groups with cyclic point group." Journal of Algebra 493 (January 2018): 79–88. http://dx.doi.org/10.1016/j.jalgebra.2017.08.035.

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19

Thomas, Oliver. "Duality for K-analytic Group Cohomology of p-adic Lie Groups." Comptes Rendus. Mathématique 360, G11 (December 8, 2022): 1213–26. http://dx.doi.org/10.5802/crmath.373.

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20

Raghuram, A. "A Künneth Theorem for p-Adic Groups." Canadian Mathematical Bulletin 50, no. 3 (September 1, 2007): 440–46. http://dx.doi.org/10.4153/cmb-2007-043-5.

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AbstractLet G1 and G2 be p-adic groups. We describe a decomposition of Ext-groups in the category of smooth representations of G1 × G2 in terms of Ext-groups for G1 and G2. We comment on for a supercuspidal representation π of a p-adic group G. We also consider an example of identifying the class, in a suitable Ext1, of a Jacquet module of certain representations of p-adic GL2n.
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21

Loeffler, David, and Sarah Livia Zerbes. "Iwasawa theory and p-adic L-functions over ${\mathbb Z}_{p}^{2}$-extensions." International Journal of Number Theory 10, no. 08 (October 29, 2014): 2045–95. http://dx.doi.org/10.1142/s1793042114500699.

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We construct a two-variable analogue of Perrin-Riou's p-adic regulator map for the Iwasawa cohomology of a crystalline representation of the absolute Galois group of ℚp, over a Galois extension whose Galois group is an abelian p-adic Lie group of dimension 2. We use this regulator map to study p-adic representations of global Galois groups over certain abelian extensions of number fields whose localization at the primes above p is an extension of the above type. In the example of the restriction to an imaginary quadratic field of the representation attached to a modular form, we formulate a conjecture on the existence of a "zeta element", whose image under the regulator map is a p-adic L-function. We show that this conjecture implies the known properties of the 2-variable p-adic L-functions constructed by Perrin-Riou and Kim.
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22

Missarov, M. D. "p-adic renormalization group solutions and the euclidean renormalization group conjectures." P-Adic Numbers, Ultrametric Analysis, and Applications 4, no. 2 (February 2012): 109–14. http://dx.doi.org/10.1134/s2070046612020033.

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23

Vignéras, Marie-France. "Representations modulo p of the p-adic group GL(2, F)." Compositio Mathematica 140, no. 02 (March 2004): 333–58. http://dx.doi.org/10.1112/s0010437x03000071.

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24

Adler, Jeffrey D., and Alan Roche. "An Intertwining Result for p-adic Groups." Canadian Journal of Mathematics 52, no. 3 (June 1, 2000): 449–67. http://dx.doi.org/10.4153/cjm-2000-021-8.

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AbstractFor a reductive p-adic group G, we compute the supports of the Hecke algebras for the K-types for G lying in a certain frequently-occurring class. When G is classical, we compute the intertwining between any two such K-types.
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25

Sekiguchi, Katsusuke. "On the automorphism group of the p-adic group ring of a metacyclic p-Group, II." Journal of Algebra 100, no. 1 (April 1986): 191–213. http://dx.doi.org/10.1016/0021-8693(86)90073-6.

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26

Takloo-Bighash, Ramin. "L - functions for the p-adic group GSp (4)." American Journal of Mathematics 122, no. 6 (2000): 1085–120. http://dx.doi.org/10.1353/ajm.2000.0049.

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27

Woodcock, C. F. "The Automorphism Group of a p -Adic Convolution Algebra." Journal of the London Mathematical Society 56, no. 1 (August 1997): 171–78. http://dx.doi.org/10.1112/s0024610797005371.

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28

Kochubei, Anatoly N., and Yuri Kondratiev. "Representations of the infinite-dimensional p-adic affine group." Infinite Dimensional Analysis, Quantum Probability and Related Topics 23, no. 01 (March 2020): 2050002. http://dx.doi.org/10.1142/s0219025720500022.

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We introduce an infinite-dimensional [Formula: see text]-adic affine group and construct its irreducible unitary representation. Our approach follows the one used by Vershik, Gelfand and Graev for the diffeomorphism group, but with modifications made necessary by the fact that the group does not act on the phase space. However, it is possible to define its action on some classes of functions.
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29

White, Paul-James. "p-adic Langlands functoriality for the definite unitary group." Journal für die reine und angewandte Mathematik (Crelles Journal) 2014, no. 691 (January 1, 2014): 1–27. http://dx.doi.org/10.1515/crelle-2012-0074.

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30

Campbell, Justin. "The Bernstein center of a p-adic unipotent group." Journal of Algebra 560 (October 2020): 521–37. http://dx.doi.org/10.1016/j.jalgebra.2020.04.035.

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31

DANIŞMAN, Yusuf. "Regular poles for the p-adic group $GSp_4$-II." TURKISH JOURNAL OF MATHEMATICS 39 (2015): 369–94. http://dx.doi.org/10.3906/mat-1404-72.

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32

Garuti, Marco A. "Barsotti–Tate groups and p-adic representations of the fundamental group scheme." Mathematische Annalen 341, no. 3 (January 15, 2008): 603–22. http://dx.doi.org/10.1007/s00208-007-0205-0.

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33

Pop, Florian, and Jakob Stix. "Arithmetic in the fundamental group of a p-adic curve. On the p-adic section conjecture for curves." Journal für die reine und angewandte Mathematik (Crelles Journal) 2017, no. 725 (January 1, 2017): 1–40. http://dx.doi.org/10.1515/crelle-2014-0077.

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34

Glöckner, Helge, and George A. Willis. "Locally pro-p contraction groups are nilpotent." Journal für die reine und angewandte Mathematik (Crelles Journal) 2021, no. 781 (October 16, 2021): 85–103. http://dx.doi.org/10.1515/crelle-2021-0050.

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Abstract The authors have shown previously that every locally pro-p contraction group decomposes into the direct product of a p-adic analytic factor and a torsion factor. It has long been known that p-adic analytic contraction groups are nilpotent. We show here that the torsion factor is nilpotent too, and hence that every locally pro-p contraction group is nilpotent.
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35

MEURICE, YANNICK. "QUANTUM MECHANICS WITH p-ADIC NUMBERS." International Journal of Modern Physics A 04, no. 19 (November 20, 1989): 5133–47. http://dx.doi.org/10.1142/s0217751x8900217x.

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We discuss unitary realizations of the Heisenberg group and the linear canonical transformations over a complex Hilbert space but with dynamical variables on a p-adic field Qp. For all p, an appropriate choice of phase turns the realization of the linear canonical transformation into a representation up to a sign of SL (2, Qp). We give the spectra of the subgroups corresponding to the free particle and the harmonic oscillator. We discuss briefly the possibility of an adelic interpretation.
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36

Kariyama, Kazutoshi. "On Types for Unramified p-Adic Unitary Groups." Canadian Journal of Mathematics 60, no. 5 (October 2008): 1067–107. http://dx.doi.org/10.4153/cjm-2008-048-7.

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AbstractLet F be a non-archimedean local field of residue characteristic neither 2 nor 3 equipped with a galois involution with fixed field F0, and let G be a symplectic group over F or an unramified unitary group over F0. Following the methods of Bushnell–Kutzko for GL(N, F), we define an analogue of a simple type attached to a certain skew simple stratum, and realize a type in G. In particular, we obtain an irreducible supercuspidal representation of G like GL(N, F).
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37

Henniart, Guy, and Marie-France Vignéras. "Representations of a reductive p-adic group in characteristic distinct from p." Tunisian Journal of Mathematics 4, no. 2 (August 24, 2022): 249–305. http://dx.doi.org/10.2140/tunis.2022.4.249.

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38

ALBEVERIO, SERGIO, and ANDREW KHRENNIKOV. "p-ADIC HILBERT SPACE REPRESENTATION OF QUANTUM SYSTEMS WITH AN INFINITE NUMBER OF DEGREES OF FREEDOM." International Journal of Modern Physics B 10, no. 13n14 (June 30, 1996): 1665–73. http://dx.doi.org/10.1142/s021797929600074x.

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Gaussian measures on infinite-dimensional p-adic spaces are introduced and the corresponding L2-spaces of p-adic valued square integrable functions are constructed. Representations of the infinite-dimensional Weyl group are realized in p-adic L2-spaces. p-adic Hilbert space representations of quantum Hamiltonians for systems with an infinite number of degrees of freedom are constructed. Many Hamiltonians with potentials which are too singular to exist as functions over reals are realized as bounded symmetric operators in L2-spaces with respect to a p-adic Gaussian measure.
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39

CHEKHOV, L. O., A. D. MIRONOV, and A. V. ZABRODIN. "MULTILOOP CALCULUS IN P-ADIC STRING THEORY AND BRUHAT-TITS TREES." Modern Physics Letters A 04, no. 13 (July 10, 1989): 1227–35. http://dx.doi.org/10.1142/s0217732389001428.

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We treat the open p-adic string world sheet as a coset space F=T/Γ, where T is the Bruhat-Tits tree for the p-adic linear group GL (2, ℚp) and Γ⊂ PGL (2, ℚp) is some Schottky group. The boundary of this world sheet corresponds to p-adic Mumford curve of finite genus. The string dynamics is governed by the local gaussian action on the tree T. We find the amplitudes for emission processes of the tachyon states from the boundary.
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40

Moy, Allen. "Distribution Algebras on p-adic Groups and Lie Algebras." Canadian Journal of Mathematics 63, no. 5 (October 18, 2011): 1137–60. http://dx.doi.org/10.4153/cjm-2011-025-3.

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Abstract When F is a p-adic field, and is the group of F-rational points of a connected algebraic F-group, the complex vector space of compactly supported locally constant distributions on G has a natural convolution product that makes it into a ℂ-algebra (without an identity) called the Hecke algebra. The Hecke algebra is a partial analogue for p-adic groups of the enveloping algebra of a Lie group. However, has drawbacks such as the lack of an identity element, and the process is not a functor. Bernstein introduced an enlargement . The algebra consists of the distributions that are left essentially compact. We show that the process is a functor. If is a morphism of p-adic groups, let be the morphism of ℂ-algebras. We identify the kernel of in terms of Ker. In the setting of p-adic Lie algebras, with g a reductive Lie algebra, m a Levi, and the natural projection, we show that maps G-invariant distributions on to NG(m)-invariant distributions on m. Finally, we exhibit a natural family of G-invariant essentially compact distributions on g associated with a G-invariant non-degenerate symmetric bilinear form on g and in the case of SL(2) show how certain members of the family can be moved to the group.
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41

BERGER, TOBIAS, and KRZYSZTOF KLOSIN. "A p-ADIC HERMITIAN MAASS LIFT." Glasgow Mathematical Journal 61, no. 1 (April 17, 2018): 85–114. http://dx.doi.org/10.1017/s0017089518000071.

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AbstractFor K, an imaginary quadratic field with discriminant −DK, and associated quadratic Galois character χK, Kojima, Gritsenko and Krieg studied a Hermitian Maass lift of elliptic modular cusp forms of level DK and nebentypus χK via Hermitian Jacobi forms to Hermitian modular forms of level one for the unitary group U(2, 2) split over K. We generalize this (under certain conditions on K and p) to the case of p-oldforms of level pDK and character χK. To do this, we define an appropriate Hermitian Maass space for general level and prove that it is isomorphic to the space of special Hermitian Jacobi forms. We then show how to adapt this construction to lift a Hida family of modular forms to a p-adic analytic family of automorphic forms in the Maass space of level p.
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42

Bhandari, A. K., and S. K. Sehgal. "An Induction Theorem for Units of p-Adic Group Rings." Canadian Mathematical Bulletin 34, no. 1 (March 1, 1991): 31–35. http://dx.doi.org/10.4153/cmb-1991-005-8.

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AbstractLet G be a finite group and let C be the family of cyclic subgroups of G. We show that the normal subgroup H of U = U(ZpG) generated by U(ZpC), C ∊ C, where Zp is the ring of p-adic integers, is of finite index in U.
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43

Morris, Sidney A., and Sheila Oates-Williams. "A Characterization of the Topological Group of p -Adic Integers." Bulletin of the London Mathematical Society 19, no. 1 (January 1987): 57–59. http://dx.doi.org/10.1112/blms/19.1.57.

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44

Roggenkamp, Klaus W. "Subgroup Rigidity of p -Adic Group Rings (Weiss Arguments Revisited)." Journal of the London Mathematical Society s2-46, no. 3 (December 1992): 432–48. http://dx.doi.org/10.1112/jlms/s2-46.3.432.

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45

Feldman, G. M. "The Heyde theorem on the group of p-adic numbers." Doklady Mathematics 89, no. 3 (May 2014): 359–61. http://dx.doi.org/10.1134/s1064562414030259.

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46

Yang, Zhiqing. "A construction of classifying spaces for p-adic group actions." Topology and its Applications 153, no. 1 (August 2005): 161–70. http://dx.doi.org/10.1016/j.topol.2005.01.029.

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47

Karpuk, David A. "Cohomology of the Weil group of a p -adic field." Journal of Number Theory 133, no. 4 (April 2013): 1270–88. http://dx.doi.org/10.1016/j.jnt.2012.08.028.

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48

Hoechsmann, Klaus, and Jürgen Ritter. "The Artin-Hasse power series and p-adic group rings." Journal of Number Theory 39, no. 1 (September 1991): 117–28. http://dx.doi.org/10.1016/0022-314x(91)90039-e.

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49

Aubert, Anne-Marie, and Roger Plymen. "Explicit Plancherel formula for the p-adic group GL(n)." Comptes Rendus Mathematique 338, no. 11 (June 2004): 843–48. http://dx.doi.org/10.1016/j.crma.2004.03.026.

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50

Backhausz, Tibor, and Gergely Zábrádi. "Algebraic functional equations and completely faithful Selmer groups." International Journal of Number Theory 11, no. 04 (April 29, 2015): 1233–57. http://dx.doi.org/10.1142/s1793042115500670.

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Let E be an elliptic curve — defined over a number field K — without complex multiplication and with good ordinary reduction at all the primes above a rational prime p ≥ 5. We construct a pairing on the dual p∞-Selmer group of E over any strongly admissible p-adic Lie extension K∞/K under the assumption that it is a torsion module over the Iwasawa algebra of the Galois group G = Gal(K∞/K). Under some mild additional hypotheses, this gives an algebraic functional equation of the conjectured p-adic L-function. As an application, we construct completely faithful Selmer groups in case the p-adic Lie extension is obtained by adjoining the p-power division points of another non-CM elliptic curve A.
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