A representation of twisted group algebra of symmetric groups on weight subspaces of free associative complex algebra

2015/04/08 by Milena Sošić, Sosic, Milena
Mathematics · Physics and Astronomy · #05E10 #Advanced Topics in Algebra #Algebraic structures and combinatorial models #FOS: Mathematics #Nonlinear Waves and Solitons #Representation Theory (math.RT)

paper · pdf · doi:10.48550/arxiv.1504.01941

openalex publication_date 2015/04/08 · openalex created_date 2016/06/24 · openalex updated_date 2026/07/28

Abstract

Here we consider two algebras, a free unital associative complex algebra (denoted by B) equiped with a multiparametric q-differential structure and a twisted group algebra (denoted by A(S_n)), with the motivation to represent the algebra A(S_n) on the (generic) weight subpaces of the algebra B. One of the fundamental problems in B is to describe the space of all constants (the elements which are annihilated by all multiparametric partial derivatives). To solve this problem, one needs some special matrices and their factorizations in terms of simpler matrices. A simpler approach is to study first certain canonical elements in the twisted group algebra A(S_n). Then one can use certain natural representation of A(S_n) on the weight subspaces of B, which are the subject of this paper.

Citations

• Determinants and Inversion of Gram Matrices in Fock Representation of \q_kl\- Canonical Commutation Relations and Applications to Hyperplane Arrangements and Quantum Groups. Proof of an Extension of Zagier's Conjecture

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• Some factorizations in the twisted group algebra of symmetric groups
• Representations of twisted tensor products
• Algebra of double cosets of a symmetric group by a smaller symmetric group
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