The finite dimensional irreducible modules for affine walled Brauer algebras

2021 ◽  
Author(s):  
Mei Si
Keyword(s):  
Finite Dimensional ◽  
Irreducible Modules ◽  
Brauer Algebras

scholarly journals Cyclotomic Nazarov-Wenzl Algebras

2006 ◽  
Vol 182 ◽  
pp. 47-134 ◽  
Author(s):  
Susumu Ariki ◽  
Andrew Mathas ◽  
Hebing Rui
Keyword(s):  
Irreducible Representations ◽  
Arbitrary Field ◽  
Dimensional Algebra ◽  
Simple Modules ◽  
Infinite Dimensional ◽  
Finite Dimensional ◽  
Irreducible Modules ◽  
Brauer Algebras

AbstractNazarov [Naz96] introduced an infinite dimensional algebra, which he called the affine Wenzl algebra, in his study of the Brauer algebras. In this paper we study certain “cyclotomic quotients” of these algebras. We construct the irreducible representations of these algebras in the generic case and use this to show that these algebras are free of rank rn(2n−1)!! (when Ω is u-admissible). We next show that these algebras are cellular and give a labelling for the simple modules of the cyclotomic Nazarov-Wenzl algebras over an arbitrary field. In particular, this gives a construction of all of the finite dimensional irreducible modules of the affine Wenzl algebra.

On basic Cycles of An, Bn, Cn and Dn

1985 ◽  
Vol 37 (1) ◽  
pp. 122-140 ◽  
Author(s):  
D. J. Britten ◽  
F. W. Lemire
Keyword(s):  
Lie Algebra ◽  
Dual Space ◽  
Cartan Subalgebra ◽  
Closed Field ◽  
Generating Set ◽  
Enveloping Algebra ◽  
Simple Lie Algebra ◽  
Finite Dimensional ◽  
Irreducible Modules ◽  
Positive Roots

In this paper, we investigate a conjecture of Dixmier [2] on the structure of basic cycles. Our interest in basic cycles arises primarily from the fact that the irreducible modules of a simple Lie algebra L having a weight space decomposition are completely determined by the irreducible modules of the cycle subalgebra of L. The basic cycles form a generating set for the cycle subalgebra.First some notation: F denotes an algebraically closed field of characteristic 0, L a finite dimensional simple Lie algebra of rank n over F, H a fixed Cartan subalgebra, U(L) the universal enveloping algebra of L, C(L) the centralizer of H in U(L), Φ the set of nonzero roots in H*, the dual space of H, Δ = {α1, …, αn} a base of Φ, and Φ+ = {β1, …, βm} the positive roots corresponding to Δ.

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 Theq-Tetrahedron Algebra and Its Finite Dimensional Irreducible Modules

2007 ◽  
Vol 35 (11) ◽  
pp. 3415-3439 ◽  
Author(s):  
Tatsuro Ito ◽  
Paul Terwilliger
Keyword(s):  
Finite Dimensional ◽  
Irreducible Modules

Cohomology of Lie Conformal Algebra Vir⋉Cur g

2021 ◽  
Vol 28 (03) ◽  
pp. 507-520
Author(s):  
Maosen Xu ◽  
Yan Tan ◽  
Zhixiang Wu
Keyword(s):  
Lie Algebra ◽  
Conformal Algebra ◽  
Cohomology Groups ◽  
Simple Lie Algebra ◽  
Finite Dimensional ◽  
Irreducible Modules

In this article, we compute cohomology groups of the semisimple Lie conformal algebra [Formula: see text] with coefficients in its irreducible modules for a finite-dimensional simple Lie algebra [Formula: see text].

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