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Journal articles on the topic 'Ariki-Koike algebras'

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Author: Grafiati

Published: 4 June 2021

Last updated: 21 February 2023

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1

Jacon, Nicolas, and Cédric Lecouvey. "Cores of Ariki-Koike algebras." Documenta Mathematica 26 (2021): 103–24. http://dx.doi.org/10.4171/dm/810.

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2

Halverson, Tom, and Arun Ram. "Murnaghan-Nakayama Rules for Characters of Iwahori-Hecke Algebras of the Complex Reflection Groups G(r, p, n)." Canadian Journal of Mathematics 50, no. 1 (February 1, 1998): 167–92. http://dx.doi.org/10.4153/cjm-1998-009-x.

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AbstractIwahori-Hecke algebras for the infinite series of complex reflection groups G(r, p, n) were constructed recently in the work of Ariki and Koike [AK], Broué andMalle [BM], and Ariki [Ari]. In this paper we give Murnaghan-Nakayama type formulas for computing the irreducible characters of these algebras. Our method is a generalization of that in our earlier paper [HR] in whichwe derivedMurnaghan-Nakayama rules for the characters of the Iwahori-Hecke algebras of the classical Weyl groups. In both papers we have been motivated by C. Greene [Gre], who gave a new derivation of the Murnaghan-Nakayama formula for irreducible symmetric group characters by summing diagonal matrix entries in Young's seminormal representations. We use the analogous representations of the Iwahori-Hecke algebra of G(r, p, n) given by Ariki and Koike [AK] and Ariki [Ari].

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3

Du, Jie, and Hebing Rui. "SPECHT MODULES FOR ARIKI-KOIKE ALGEBRAS." Communications in Algebra 29, no. 10 (August 31, 2001): 4701–19. http://dx.doi.org/10.1081/agb-100106782.

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4

Rostam, Salim. "Stuttering blocks of Ariki–Koike algebras." Algebraic Combinatorics 2, no. 1 (2019): 75–118. http://dx.doi.org/10.5802/alco.40.

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5

Du, Jie, and Hebing Rui. "Ariki-Koike algebras with semisimple bottoms." Mathematische Zeitschrift 234, no. 4 (August 1, 2000): 807–30. http://dx.doi.org/10.1007/s002090050009.

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6

Dipper, Richard, and Andrew Mathas. "Morita equivalences of Ariki-Koike algebras." Mathematische Zeitschrift 240, no. 3 (July 1, 2002): 579–610. http://dx.doi.org/10.1007/s002090100371.

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7

Fayers, Matthew. "Core blocks of Ariki–Koike algebras." Journal of Algebraic Combinatorics 26, no. 1 (January 10, 2007): 47–81. http://dx.doi.org/10.1007/s10801-006-0048-x.

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8

Yang, Guiyu. "Nil-Coxeter algebras and nil-Ariki-Koike algebras." Frontiers of Mathematics in China 10, no. 6 (September 21, 2015): 1473–81. http://dx.doi.org/10.1007/s11464-015-0498-3.

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9

Sakamoto, Masahiro, and Toshiaki Shoji. "Schur–Weyl Reciprocity for Ariki–Koike Algebras." Journal of Algebra 221, no. 1 (November 1999): 293–314. http://dx.doi.org/10.1006/jabr.1999.7973.

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10

Sawada, Nobuharu, and Toshiaki Shoji. "Modified Ariki-Koike algebras and cyclotomic q-Schur algebras." Mathematische Zeitschrift 249, no. 4 (January 7, 2005): 829–67. http://dx.doi.org/10.1007/s00209-004-0739-8.

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11

Shoji, Toshiaki, and Kentaro Wada. "Cyclotomic $q$-Schur algebras associated to the Ariki-Koike algebra." Representation Theory of the American Mathematical Society 14, no. 11 (May 6, 2010): 379–416. http://dx.doi.org/10.1090/s1088-4165-10-00375-4.

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12

Chlouveraki, Maria. "Rouquier blocks of the cyclotomic Ariki–Koike algebras." Algebra & Number Theory 2, no. 6 (October 14, 2008): 689–720. http://dx.doi.org/10.2140/ant.2008.2.689.

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13

Jacon, Nicolas, and Cédric Lecouvey. "On the Mullineux involution for Ariki–Koike algebras." Journal of Algebra 321, no. 8 (April 2009): 2156–70. http://dx.doi.org/10.1016/j.jalgebra.2008.09.033.

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14

Gerber, Thomas. "Generalised canonical basic sets for Ariki–Koike algebras." Journal of Algebra 413 (September 2014): 364–401. http://dx.doi.org/10.1016/j.jalgebra.2014.04.010.

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15

Kang, Seok-Jin, In-Sok Lee, Kyu-Hwan Lee, and Hyekyung Oh. "Representations of Ariki–Koike algebras and Gröbner–Shirshov bases." Proceedings of the London Mathematical Society 89, no. 01 (June 30, 2004): 54–70. http://dx.doi.org/10.1112/s0024611503014606.

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16

Li, Yanbo, and Dashu Xu. "Radicals of weight one blocks of Ariki–Koike algebras." Communications in Algebra 48, no. 9 (April 10, 2020): 3771–79. http://dx.doi.org/10.1080/00927872.2020.1746323.

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17

Fayers, Matthew. "Weights of multipartitions and representations of Ariki–Koike algebras." Advances in Mathematics 206, no. 1 (October 2006): 112–44. http://dx.doi.org/10.1016/j.aim.2005.07.017.

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18

Wada, Kentaro. "The representation type of Ariki–Koike algebras and cyclotomic q-Schur algebras." Advances in Mathematics 224, no. 2 (June 2010): 539–60. http://dx.doi.org/10.1016/j.aim.2009.12.003.

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19

Shoji, Toshiaki. "A Frobenius Formula for the Characters of Ariki–Koike Algebras." Journal of Algebra 226, no. 2 (April 2000): 818–56. http://dx.doi.org/10.1006/jabr.1999.8178.

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20

Mathas, Andrew. "Matrix units and generic degrees for the Ariki–Koike algebras." Journal of Algebra 281, no. 2 (November 2004): 695–730. http://dx.doi.org/10.1016/j.jalgebra.2004.07.021.

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21

Stoll, Friederike. "On the action of Ariki–Koike algebras on tensor space." Journal of Algebra 319, no. 8 (April 2008): 3352–81. http://dx.doi.org/10.1016/j.jalgebra.2007.10.008.

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22

Hu, Jun, and Friederike Stoll. "On double centralizer properties between quantum groups and Ariki–Koike algebras." Journal of Algebra 275, no. 1 (May 2004): 397–418. http://dx.doi.org/10.1016/j.jalgebra.2003.10.026.

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23

YAMANAKA, HITOSHI. "WEIGHTS OF MARKOV TRACES OF ALEXANDER POLYNOMIALS FOR MIXED LINKS." Journal of Knot Theory and Its Ramifications 22, no. 07 (June 2013): 1350028. http://dx.doi.org/10.1142/s0218216513500284.

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Using the Fourier expansion of Markov traces for Ariki–Koike algebras over ℚ(q, u1, …, ue), we give a direct definition of the Alexander polynomials for mixed links. We observe that under the corresponding specialization of a Markov parameter, the Fourier coefficients of Markov traces take quite a simple form. As a consequence, we show that the Alexander polynomial of a mixed link is essentially equal to the Alexander polynomial of the link obtained by resolving the twisted parts.

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24

LI, YANBO. "JUCYS–MURPHY ELEMENTS AND CENTRES OF CELLULAR ALGEBRAS." Bulletin of the Australian Mathematical Society 85, no. 2 (December 15, 2011): 261–70. http://dx.doi.org/10.1017/s0004972711002851.

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AbstractLet R be an integral domain and A a cellular algebra over R with a cellular basis {CλS,T∣λ∈Λ and S,T∈M(λ)}. Suppose that A is equipped with a family of Jucys–Murphy elements which satisfy the separation condition in the sense of Mathas [‘Seminormal forms and Gram determinants for cellular algebras’, J. reine angew. Math.619 (2008), 141–173, with an appendix by M. Soriano]. Let K be the field of fractions of R and AK=A⨂ RK. We give a necessary and sufficient condition under which the centre of AK consists of the symmetric polynomials in Jucys–Murphy elements. We also give an application of our result to Ariki–Koike algebras.

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25

Lacabanne, Abel, and Pedro Vaz. "Schur–Weyl duality, Verma modules, and row quotients of Ariki–Koike algebras." Pacific Journal of Mathematics 311, no. 1 (March 17, 2021): 113–33. http://dx.doi.org/10.2140/pjm.2021.311.113.

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26

Schoennenbeck, Christoph. "On the number of constituents of induced modules of Ariki-Koike algebras." Journal of Algebra 544 (February 2020): 125–50. http://dx.doi.org/10.1016/j.jalgebra.2019.09.029.

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27

Lyle, Sinéad, and Oliver Ruff. "Graded decomposition numbers of Ariki–Koike algebras for blocks of small weight." Journal of Pure and Applied Algebra 220, no. 6 (June 2016): 2112–42. http://dx.doi.org/10.1016/j.jpaa.2015.10.019.

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28

Fayers, Matthew. "Weights of multipartitions and representations of Ariki–Koike algebras II: Canonical bases." Journal of Algebra 319, no. 7 (April 2008): 2963–78. http://dx.doi.org/10.1016/j.jalgebra.2007.10.002.

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29

Ariki, Susumu, Nicolas Jacon, and Cédric Lecouvey. "Factorization of the canonical bases for higher-level Fock spaces." Proceedings of the Edinburgh Mathematical Society 55, no. 1 (June 20, 2011): 23–51. http://dx.doi.org/10.1017/s0013091510000519.

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AbstractThe level l Fock space admits canonical bases $\mathcal{G}_{e}$ and $\smash{\mathcal{G}_{\infty}}$. They correspond to $\smash{\mathcal{U}_{v}(\widehat{\mathfrak{sl}}_{e})}$ and $\mathcal{U}_{v}({\mathfrak{sl}}_{\infty})$-module structures. We establish that the transition matrices relating these two bases are unitriangular with coefficients in ℕ[v]. Restriction to the highest-weight modules generated by the empty l-partition then gives a natural quantization of a theorem by Geck and Rouquier on the factorization of decomposition matrices which are associated to Ariki–Koike algebras.

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30

Jacon, Nicolas. "On the one dimensional representations of Ariki–Koike algebras at roots of unity." Journal of Pure and Applied Algebra 221, no. 6 (June 2017): 1298–315. http://dx.doi.org/10.1016/j.jpaa.2016.09.012.

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31

Foda, Omar, Bernard Leclerc, Masato Okado, Jean-Yves Thibon, and Trevor A. Welsh. "Branching Functions ofA(1)n−1and Jantzen–Seitz Problem for Ariki–Koike Algebras." Advances in Mathematics 141, no. 2 (February 1999): 322–65. http://dx.doi.org/10.1006/aima.1998.1783.

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32

Jacon, Nicolas. "An algorithm for the computation of the decomposition matrices for Ariki–Koike algebras." Journal of Algebra 292, no. 1 (October 2005): 100–109. http://dx.doi.org/10.1016/j.jalgebra.2004.10.017.

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33

Hivert, Florent, Jean-Christophe Novelli, and Jean-Yves Thibon. "Yang–Baxter bases of 0-Hecke algebras and representation theory of 0-Ariki–Koike–Shoji algebras." Advances in Mathematics 205, no. 2 (October 2006): 504–48. http://dx.doi.org/10.1016/j.aim.2005.07.016.

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34

Jacon, Nicolas. "On the parametrization of the simple modules for Ariki-Koike algebras at roots of unity." Journal of Mathematics of Kyoto University 44, no. 4 (2004): 729–67. http://dx.doi.org/10.1215/kjm/1250281696.

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35

Jacon, Nicolas. "Crystal Graphs of Higher Level q-deformed Fock Spaces, Lusztig a-values and Ariki–Koike Algebras." Algebras and Representation Theory 10, no. 6 (July 28, 2007): 565–91. http://dx.doi.org/10.1007/s10468-007-9081-2.

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36

Mak, Chi Kin. "A Reducibility Theorem ofG(m, 1,r) and Its Application to Trace Functions on Ariki–Koike Algebras." Communications in Algebra 36, no. 3 (March 7, 2008): 973–91. http://dx.doi.org/10.1080/00927870701776730.

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37

Chlouveraki, Maria, and Nicolas Jacon. "Schur elements for the Ariki–Koike algebra and applications." Journal of Algebraic Combinatorics 35, no. 2 (September 27, 2011): 291–311. http://dx.doi.org/10.1007/s10801-011-0314-4.

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38

Armon, Sam, and Tom Halverson. "Transition Matrices Between Young's Natural and Seminormal Representations." Electronic Journal of Combinatorics 28, no. 3 (July 16, 2021). http://dx.doi.org/10.37236/10081.

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We derive a formula for the entries in the change-of-basis matrix between Young's seminormal and natural representations of the symmetric group. These entries are determined as sums over weighted paths in the weak Bruhat graph on standard tableaux, and we show that they can be computed recursively as the weighted sum of at most two previously-computed entries in the matrix. We generalize our results to work for affine Hecke algebras, Ariki-Koike algebras, Iwahori-Hecke algebras, and complex reflection groups given by the wreath product of a finite cyclic group with the symmetric group.

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39

Ohkura, Kiyotaka, and Toshiaki Shoji. "On certain bases for Ariki-Koike algebras arising from canonical bases for Uv(slm)." SUT Journal of Mathematics 38, no. 2 (June 1, 2002). http://dx.doi.org/10.55937/sut/1057898725.

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