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Journal articles on the topic 'Highest weight modules'

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Published: 6 September 2023
Last updated: 7 September 2023

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1

Adams, Jeffrey. "Unitary highest weight modules." Advances in Mathematics 63, no. 2 (February 1987): 113–37. http://dx.doi.org/10.1016/0001-8708(87)90049-1.

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2

Matumoto, Hisayosi. "Whittaker modules associated with highest weight modules." Duke Mathematical Journal 60, no. 1 (February 1990): 59–113. http://dx.doi.org/10.1215/s0012-7094-90-06002-8.

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3

Dimitrov, I., and I. Penkov. "Partially integrable highest weight modules." Transformation Groups 3, no. 3 (September 1998): 241–53. http://dx.doi.org/10.1007/bf01236874.

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4

Chen, Guobo. "A Family of Non-weight Modules over the Virasoro Algebra." Algebra Colloquium 27, no. 04 (November 5, 2020): 807–20. http://dx.doi.org/10.1142/s100538672000067x.

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In this paper, we consider the tensor product modules of a class of non-weight modules and highest weight modules over the Virasoro algebra. We determine the necessary and sufficient conditions for such modules to be simple and the isomorphism classes among all these modules. Finally, we prove that these simple non-weight modules are new if the highest weight module over the Virasoro algebra is non-trivial.
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5

Grishkov, A. N., and F. Marko. "Description of costandard modules for Schur superalgebra S(2|2) in positive characteristic." Journal of Algebra and Its Applications 17, no. 02 (January 23, 2018): 1850038. http://dx.doi.org/10.1142/s021949881850038x.

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In this paper, we shall describe costandard modules [Formula: see text] of restricted highest weight [Formula: see text] for Schur superalgebra [Formula: see text] over an algebraically closed field [Formula: see text] of positive characteristic [Formula: see text]. Additionally, for a restricted highest weight [Formula: see text], we determine all composition factors of the costandard module [Formula: see text]; in particular we compute the decomposition numbers in the process of the modular reduction of a simple module with a restricted highest weight.
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6

Matumoto, Hisayosi. "Correction to Whittaker modules associated with highest weight modules." Duke Mathematical Journal 61, no. 3 (December 1990): 973. http://dx.doi.org/10.1215/s0012-7094-90-06137-x.

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7

Mazorchuk, Volodymyr, and Kaiming Zhao. "Characterization of Simple Highest Weight Modules." Canadian Mathematical Bulletin 56, no. 3 (September 1, 2013): 606–14. http://dx.doi.org/10.4153/cmb-2011-199-5.

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Abstract.We prove that for simple complex finite dimensional Lie algebras, affine Kac–Moody Lie algebras, the Virasoro algebra, and the Heisenberg–Virasoro algebra, simple highest weight modules are characterized by the property that all positive root elements act on these modules locally nilpotently. We also show that this is not the case for higher rank Virasoro algebras and for Heisenberg algebras.
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8

Boyallian, Carina, and Vanesa Meinardi. "Quasi-finite highest weight modules overWN∞." Journal of Physics A: Mathematical and Theoretical 44, no. 23 (May 6, 2011): 235201. http://dx.doi.org/10.1088/1751-8113/44/23/235201.

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9

Huang, Jing-Song, and Wei Xiao. "Dirac cohomology of highest weight modules." Selecta Mathematica 18, no. 4 (January 17, 2012): 803–24. http://dx.doi.org/10.1007/s00029-011-0085-8.

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10

Neeb, Karl-Hermann. "Square integrable highest weight representations." Glasgow Mathematical Journal 39, no. 3 (September 1997): 296–321. http://dx.doi.org/10.1017/s0017089500032237.

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If G is the group of holomorphic automorphisms of a bounded symmetric domain, then G has a distinguished class of irreducible unitary representations called the holomorphic discrete series of G. These representations have been studied by Harish-Chandra in [7]. On the Lie algebra level, the Harish-Chandra modules corresponding to the holomorphic discrete series representations are highest weight modules. Even for G as above, it turns out that not all the unitary highest weight modules belong to the holomorphic discrete series but there exists a condition on the highest weight which characterizes the holomorphic discrete series among the unitary highest weight representations. They can be defined as those unitary highest weight representations with square integrable matrix coefficients.
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11

Lin, Weiqiang, and Yucai Su. "Quasi-finite Irreducible Graded Modules for the Virasoro-like Algebra." Algebra Colloquium 20, no. 02 (April 3, 2013): 181–96. http://dx.doi.org/10.1142/s1005386713000175.

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In this paper, we consider the classification of irreducible Z- and Z2-graded modules with finite-dimensional homogeneous subspaces over the Virasoro-like algebra. We prove that such a module is a uniformly bounded module or a generalized highest weight module. Then we determine all generalized highest weight quasi-finite irreducible modules. As a consequence, we determine all the modules with nonzero center. Finally, we prove that there does not exist any non-trivial Z-graded module of intermediate series.
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12

Kawasetsu, Kazuya. "Relaxed highest-weight modules III: Character formulae." Advances in Mathematics 393 (December 2021): 108079. http://dx.doi.org/10.1016/j.aim.2021.108079.

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13

Futorny, V., and V. Mazorchuk. "Highest weight categories of Lie algebra modules." Journal of Pure and Applied Algebra 138, no. 2 (May 1999): 107–18. http://dx.doi.org/10.1016/s0022-4049(97)00214-4.

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14

Gorelik, Maria, and Dimitar Grantcharov. "Bounded Highest Weight Modules Over 𝔮(n)." International Mathematics Research Notices 2014, no. 22 (July 26, 2013): 6111–54. http://dx.doi.org/10.1093/imrn/rnt147.

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15

Krötz, Bernhard. "Norm estimates for unitarizable highest weight modules." Annales de l’institut Fourier 49, no. 4 (1999): 1241–64. http://dx.doi.org/10.5802/aif.1716.

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16

Khare, Apoorva. "Standard parabolic subsets of highest weight modules." Transactions of the American Mathematical Society 369, no. 4 (June 20, 2016): 2363–94. http://dx.doi.org/10.1090/tran/6710.

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17

Zapletal, A. "Difference equations and highest-weight modules of." Journal of Physics A: Mathematical and General 31, no. 47 (November 27, 1998): 9593–600. http://dx.doi.org/10.1088/0305-4470/31/47/018.

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18

Zierau, Roger. "Geometric construction of certain highest weight modules." Proceedings of the American Mathematical Society 95, no. 4 (April 1, 1985): 631. http://dx.doi.org/10.1090/s0002-9939-1985-0810176-1.

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19

Karolinsky, E., A. Stolin, and V. Tarasov. "Irreducible highest weight modules and equivariant quantization." Advances in Mathematics 211, no. 1 (May 2007): 266–83. http://dx.doi.org/10.1016/j.aim.2006.08.004.

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20

Enright, Thomas J., and Brad Shelton. "Decompositions in categories of highest weight modules." Journal of Algebra 100, no. 2 (May 1986): 380–402. http://dx.doi.org/10.1016/0021-8693(86)90083-9.

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21

Ben-Zvi, David, Sam Gunningham, and Hendrik Orem. "Highest Weights for Categorical Representations." International Mathematics Research Notices 2020, no. 24 (December 5, 2018): 9988–10004. http://dx.doi.org/10.1093/imrn/rny258.

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Abstract We present a criterion for establishing Morita equivalence of monoidal categories and apply it to the categorical representation theory of reductive groups $G$. We show that the “de Rham group algebra” $\mathcal D(G)$ (the monoidal category of $\mathcal D$-modules on $G$) is Morita equivalent to the universal Hecke category $\mathcal D({N}\backslash{G}/{N})$ and to its monodromic variant $\widetilde{\mathcal D}({B}\backslash{G}/{B})$. In other words, de Rham $G$-categories, that is, module categories for $\mathcal D(G)$, satisfy a “highest weight theorem”—they all appear in the decomposition of the universal principal series representation $\mathcal D(G/N)$ or in twisted $\mathcal D$-modules on the flag variety $\widetilde{\mathcal D}(G/B)$.
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22

Kwon, Namhee. "Vanishing Property of BRST Cohomology for Modified Highest Weight Modules." Axioms 12, no. 6 (June 2, 2023): 550. http://dx.doi.org/10.3390/axioms12060550.

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We construct certain modified highest weight modules which are called quasi highest weight modules in this paper. Using the quasi highest weight modules, we introduce a new category of modules over an affine Lie superalgebra which contains projective covers. We also prove that both these projective covers and the quasi highest weight modules satisfy the vanishing property of BRST cohomology.
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23

Lorch, John D. "An Integral Transform and Unitary Highest Weight Modules." Proceedings of the London Mathematical Society 81, no. 1 (July 2000): 93–112. http://dx.doi.org/10.1112/s0024611500012491.

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24

Pillen, Cornelius. "Tensor products of modules with restricted highest weight." Communications in Algebra 21, no. 10 (January 1993): 3647–61. http://dx.doi.org/10.1080/00927879308824754.

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25

KITAGAWA, MASATOSHI. "STABILITY OF BRANCHING LAWS FOR HIGHEST WEIGHT MODULES." Transformation Groups 19, no. 4 (October 19, 2014): 1027–50. http://dx.doi.org/10.1007/s00031-014-9284-7.

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26

Ardonne, Eddy, Rinat Kedem, and Michael Stone. "Fermionic Characters and Arbitrary Highest-Weight Integrable -Modules." Communications in Mathematical Physics 264, no. 2 (February 10, 2006): 427–64. http://dx.doi.org/10.1007/s00220-005-1486-3.

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27

Joseph, Anthony. "A surjectivity theorem for rigid highest weight modules." Inventiones Mathematicae 92, no. 3 (October 1988): 567–96. http://dx.doi.org/10.1007/bf01393748.

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28

Kawasetsu, Kazuya, and David Ridout. "Relaxed Highest-Weight Modules I: Rank 1 Cases." Communications in Mathematical Physics 368, no. 2 (February 4, 2019): 627–63. http://dx.doi.org/10.1007/s00220-019-03305-x.

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29

Enright, Thomas J., and Anthony Joseph. "An intrinsic analysis of unitarizable highest weight modules." Mathematische Annalen 288, no. 1 (December 1990): 571–94. http://dx.doi.org/10.1007/bf01444551.

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30

Khare, Apoorva. "Faces and maximizer subsets of highest weight modules." Journal of Algebra 455 (June 2016): 32–76. http://dx.doi.org/10.1016/j.jalgebra.2016.02.004.

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31

Irving, Ronald S. "The structure of certain highest weight modules forSL3." Journal of Algebra 99, no. 2 (April 1986): 438–57. http://dx.doi.org/10.1016/0021-8693(86)90037-2.

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32

Zierau, R. "Characteristic cycles of highest weight Harish-Chandra modules." São Paulo Journal of Mathematical Sciences 12, no. 2 (September 25, 2018): 389–410. http://dx.doi.org/10.1007/s40863-018-0092-1.

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33

Zheng, Keli, and Yongzheng Zhang. "Irreducible modules with highest weight vectors over modular Witt and special Lie superalgebras." Open Mathematics 17, no. 1 (November 19, 2019): 1381–91. http://dx.doi.org/10.1515/math-2019-0117.

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Abstract Let 𝔽 be an arbitrary field of characteristic p > 2. In this paper we study irreducible modules with highest weight vectors over Witt and special Lie superalgebras of 𝔽. The same irreducible modules of general and special linear Lie superalgebras, which are the 0-th part of Witt and special Lie superalgebras in certain ℤ-grading, are also considered. Then we establish a certain connection called a P-expansion between these modules.
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34

Joseph, Anthony. "Annihilators and associated varieties of unitary highest weight modules." Annales scientifiques de l'École normale supérieure 25, no. 1 (1992): 1–45. http://dx.doi.org/10.24033/asens.1642.

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35

Dobrev, V. K. "Characters of theUq(sl(3,C)) Highest Weight Modules." Progress of Theoretical Physics Supplement 102 (1990): 137–58. http://dx.doi.org/10.1143/ptps.102.137.

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36

Meng, Guowu, and Ruibin Zhang. "Generalized MICZ-Kepler problems and unitary highest weight modules." Journal of Mathematical Physics 52, no. 4 (April 2011): 042106. http://dx.doi.org/10.1063/1.3574886.

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37

Khare, Apoorva. "Erratum to “Standard parabolic subsets of highest weight modules”." Transactions of the American Mathematical Society 369, no. 4 (December 12, 2016): 3015. http://dx.doi.org/10.1090/tran/7141.

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38

Gyoja, Akihiko. "Highest weight modules and {$b$}-functions of semi-invariants." Publications of the Research Institute for Mathematical Sciences 30, no. 3 (1994): 353–400. http://dx.doi.org/10.2977/prims/1195165904.

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39

Awata, Hidetoshi, Masafumi Fukuma, Yutaka Matsuo, and Satoru Odake. "Quasifinite highest weight modules over the superW 1+∞algebra." Communications in Mathematical Physics 170, no. 1 (May 1995): 151–79. http://dx.doi.org/10.1007/bf02099443.

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40

Blok, Rieuwert J. "Highest weight modules and polarized embeddings of shadow spaces." Journal of Algebraic Combinatorics 34, no. 1 (November 18, 2010): 67–113. http://dx.doi.org/10.1007/s10801-010-0263-3.

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41

Batra, Punita, Xiangqian Guo, Rencai Lu, and Kaiming Zhao. "Highest weight modules over pre-exp-polynomial Lie algebras." Journal of Algebra 322, no. 12 (December 2009): 4163–80. http://dx.doi.org/10.1016/j.jalgebra.2009.09.024.

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42

Hoyt, Crystal. "Regular Kac–Moody superalgebras and integrable highest weight modules." Journal of Algebra 324, no. 12 (December 2010): 3308–54. http://dx.doi.org/10.1016/j.jalgebra.2010.09.007.

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43

Pandžić, Pavle, Ana Prlić, Vladimír Souček, and Vít Tuček. "Dirac inequality for highest weight Harish-Chandra modules I." Mathematical Inequalities & Applications, no. 1 (2023): 233–65. http://dx.doi.org/10.7153/mia-2023-26-17.

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44

Pandžić, Pavle, Ana Prlić, Vladimír Souček, and Vít Tuček. "Dirac inequality for highest weight Harish-Chandra modules II." Mathematical Inequalities & Applications, no. 3 (2023): 729–60. http://dx.doi.org/10.7153/mia-2023-26-44.

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45

Malikov, Fyodor. "Quantum Groups: Singular Vectors and BGG Resolution." International Journal of Modern Physics A 07, supp01b (April 1992): 623–43. http://dx.doi.org/10.1142/s0217751x92003963.

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We prove existence of BGG resolution of an irreducible highest weight module over a quantum group, classify morphisms of Verma modules over a quantum group and find formulas for singular vectors in Verma modules. As an application we find cohomology of the quantum group of the type [Formula: see text] with coefficients in a finite-dimensional module.
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46

Eswara Rao, S., and Punita Batra. "Classification of irreducible integrable highest weight modules for current Kac–Moody algebras." Journal of Algebra and Its Applications 16, no. 07 (June 21, 2016): 1750123. http://dx.doi.org/10.1142/s0219498817501237.

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This paper classifies irreducible, integrable highest weight modules for “current Kac–Moody Algebras” with finite-dimensional weight spaces. We prove that these modules turn out to be modules of appropriate direct sums of finitely many copies of Kac–Moody Lie algebras.
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47

Britten, D. J., J. Hooper, and F. W. Lemire. "Simple Cn modules with multiplicities 1 and applications." Canadian Journal of Physics 72, no. 7-8 (July 1, 1994): 326–35. http://dx.doi.org/10.1139/p94-048.

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In this paper we show that there exist exactly two nonequivalent simple infinite dimensional highest weight Cn modules having the property that every weight space is one dimensional. The tensor products of these modules with any finite-dimensional simple Cn module are proven to be completely reducible and we provide an explicit decomposition for such tensor products. As an application of these decompositions, we obtain two recursion formulas for computing the multiplicities of simple finite dimensional Cn modules. These formulas involve a sum over subgroups of index 2 in the Weyl group of Cn.
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48

Chen, Haibo, and JianZhi Han. "A class of simple non-weight modules over the virasoro algebra." Proceedings of the Edinburgh Mathematical Society 63, no. 4 (August 7, 2020): 956–70. http://dx.doi.org/10.1017/s0013091520000279.

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AbstractThe Virasoro algebra $\mathcal {L}$ is an infinite-dimensional Lie algebra with basis {Lm, C| m ∈ ℤ} and relations [Lm, Ln] = (n − m)Lm+n + δm+n,0((m3 − m)/12)C, [Lm, C] = 0 for m, n ∈ ℤ. Let $\mathfrak a$ be the subalgebra of $\mathcal {L}$ spanned by Li for i ≥ −1. For any triple (μ, λ, α) of complex numbers with μ ≠ 0, λ ≠ 0 and any non-trivial $\mathfrak a$-module V satisfying the condition: for any v ∈ V there exists a non-negative integer m such that Liv = 0 for all i ≥ m, non-weight $\mathcal {L}$-modules on the linear tensor product of V and ℂ[∂], denoted by $\mathcal {M}(V,\mu ,\Omega (\lambda ,\alpha ))\ (\Omega (\lambda ,\alpha )=\mathbb {C}[\partial ]$ as vector spaces), are constructed in this paper. We prove that $\mathcal {M}(V,\mu ,\Omega (\lambda ,\alpha ))$ is simple if and only if μ ≠ 1, λ ≠ 0, α ≠ 0. We also give necessary and sufficient conditions for two such simple $\mathcal {L}$-modules being isomorphic. Finally, these simple $\mathcal {L}$-modules $\mathcal {M}(V,\mu ,\Omega (\lambda ,\alpha ))$ are proved to be new for V not being the highest weight $\mathfrak a$-module whose highest weight is non-zero.
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49

ALTSCHULER, DANIEL, and BRIAN DAVIES. "QUANTUM LOOP MODULES AND QUANTUM SPIN CHAINS." International Journal of Modern Physics A 09, no. 22 (September 10, 1994): 3925–58. http://dx.doi.org/10.1142/s0217751x94001588.

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We construct level-0 modules of the quantum affine algebra [Formula: see text], as the q-deformed version of the Lie algebra loop module construction. We give necessary and sufficient conditions for the modules to be irreducible. We construct the crystal base for some of these modules and find significant differences from the case of highest weight modules. We also consider the role of loop modules in the recent scheme for diagonalizing certain quantum spin chains using their [Formula: see text] symmetry.
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50

LÜ, RENCAI, and KAIMING ZHAO. "CLASSIFICATION OF IRREDUCIBLE WEIGHT MODULES OVER THE TWISTED HEISENBERG–VIRASORO ALGEBRA." Communications in Contemporary Mathematics 12, no. 02 (April 2010): 183–205. http://dx.doi.org/10.1142/s0219199710003786.

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In this paper, all irreducible weight modules with finite dimensional weight spaces over the twisted Heisenberg–Virasoro algebra are determined. There are two different classes of them. One class is formed by simple modules of intermediate series, whose nonzero weight spaces are all 1-dimensional; the other class consists of the irreducible highest weight modules and lowest weight modules.
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