Weight modules with a finite dimensional weight space over truncated Virasoro algebras

2010 ◽  
Vol 51 (12) ◽  
pp. 123522 ◽  
Author(s):  
Xiangqian Guo ◽  
Xuewen Liu
Keyword(s):  
Weight Space ◽  
Finite Dimensional ◽  
Weight Modules

scholarly journals Irreducible Weight Modules with a Finite-Dimensional Weight Space over the Twisted N = 1 Schrödinger-Neveu-Schwarz Algebra

2017 ◽  
Vol 24 (04) ◽  
pp. 697-704
Author(s):  
Huanxia Fa ◽  
Jianzhi Han ◽  
Junbo Li
Keyword(s):  
Weight Module ◽  
Weight Space ◽  
Finite Dimensional ◽  
Weight Modules

It is shown that there are no simple mixed modules over the twisted N = 1 Schrödinger-Neveu-Schwarz algebra, which implies that every irreducible weight module over it with a non-trivial finite-dimensional weight space is a Harish-Chandra module.

Simple Cn modules with multiplicities 1 and applications

1994 ◽  
Vol 72 (7-8) ◽  
pp. 326-335 ◽  
Author(s):  
D. J. Britten ◽  
J. Hooper ◽  
F. W. Lemire
Keyword(s):  
Weyl Group ◽  
Tensor Products ◽  
Weight Space ◽  
One Dimensional ◽  
Infinite Dimensional ◽  
Highest Weight ◽  
Finite Dimensional ◽  
Recursion Formulas ◽  
Completely Reducible ◽  
Index 2

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.

Note on Weight Spaces of Irreducible Linear Representations

1968 ◽  
Vol 11 (3) ◽  
pp. 399-403 ◽  
Author(s):  
F. W. Lemire
Keyword(s):  
Irreducible Representation ◽  
Weight Function ◽  
Wide Class ◽  
Irreducible Representations ◽  
Weight Space ◽  
Closed Field ◽  
One Dimensional ◽  
Highest Weight ◽  
Linear Representations ◽  
Finite Dimensional

Let L denote a finite dimensional, simple Lie algebra over an algebraically closed field F of characteristic zero. It is well known that every weight space of an irreducible representation (ρ, V) admitting a highest weight function is finite dimensional. In a previous paper [2], we have established the existence of a wide class of irreducible representations which admit a one-dimensional weight space but no highest weight function. In this paper we show that the weight spaces of all such representations are finite dimensional.

scholarly journals Classification of irreducible integrable highest weight modules for current Kac–Moody algebras

2016 ◽  
Vol 16 (07) ◽  
pp. 1750123 ◽  
Author(s):  
S. Eswara Rao ◽  
Punita Batra
Keyword(s):  
Lie Algebras ◽  
Direct Sums ◽  
Highest Weight ◽  
Finite Dimensional ◽  
Highest Weight Modules ◽  
Weight Modules

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.

scholarly journals Classification of irreducible Harish-Chandra modules over generalized Virasoro algebras

2012 ◽  
Vol 55 (3) ◽  
pp. 697-709 ◽  
Author(s):  
Xiangqian Guo ◽  
Rencai Lu ◽  
Kaiming Zhao
Keyword(s):  
Direct Summand ◽  
Virasoro Algebra ◽  
Additive Subgroup ◽  
One Dimensional ◽  
Finite Dimensional ◽  
Irreducible Modules ◽  
Intermediate Series ◽  
Complex Number Field ◽  
Weight Modules

AbstractLet G be an arbitrary non-zero additive subgroup of the complex number field ℂ, and let Vir[G] be the corresponding generalized Virasoro algebra over ℂ. In this paper we determine all irreducible weight modules with finite-dimensional weight spaces over Vir[G]. The classification strongly depends on the index group G. If G does not have a direct summand isomorphic to ℤ (the integers), then such irreducible modules over Vir[G] are only modules of intermediate series whose weight spaces are all one dimensional. Otherwise, there is one further class of modules that are constructed by using intermediate series modules over a generalized Virasoro subalgebra Vir[G0] of Vir[G] for a direct summand G0 of G with G = G0 ⊕ ℤb, where b ∈ G \ G0. This class of irreducible weight modules do not have corresponding weight modules for the classical Virasoro algebra.

scholarly journals Supports of weight modules over Witt algebras

2011 ◽  
Vol 141 (1) ◽  
pp. 155-170 ◽  
Author(s):  
Volodymyr Mazorchuk ◽  
Kaiming Zhao
Keyword(s):  
Lie Algebra ◽  
Weight Module ◽  
Root Space ◽  
Abelian Subalgebra ◽  
Space Decomposition ◽  
Finite Dimensional ◽  
Graded Lie Algebra ◽  
Alpha Beta ◽  
Weight Modules

As the first step towards a classification of simple weight modules with finite dimensional weight spaces over Witt algebras Wn, we explicitly describe the supports of such modules. We also obtain some descriptions of the support of an arbitrary simple weight module over a ℤn-graded Lie algebra $\mathfrak{g}$ having a root space decomposition $\smash{\bigoplus_{\alpha\in\mathbb{Z}^n}\mathfrak{g}_\alpha}$ with respect to the abelian subalgebra $\mathfrak{g}_0$, with the property $\smash{[\mathfrak{g}_\alpha,\mathfrak{g}_\beta] = \mathfrak{g}_{\alpha+\beta}}$ for all α, β ∈ ℤn, α ≠ β (this class contains the algebra Wn).

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