Cocharacters of UT_n(E)

2023/01/06 by Lucio Centrone, Vesselin Drensky, Centrone, Lucio +3
Mathematics · #Advanced Topics in Algebra #Algebraic structures and combinatorial models #Rings, Modules, and Algebras

paper · pdf · doi:10.48550/arxiv.2301.02566

Abstract

Let F be a field of characteristic 0 and let E be the infinite dimensional Grassmann algebra over F. In the first part of this paper we give an algorithm calculating the generating function of the cocharacter sequence of the n× n upper triangular matrix algebra UT_n(E) with entries in E, lying in a strip of a fixed size. In the second part we compute the double Hilbert series H(E;T_k,Y_l) of E, then we define the (k,l)-multiplicity series of any PI-algebra. As an application, we derive from H(E;T_k,Y_l) an easy algorithm determining the (k,l)-multiplicity series of UT_n(E).

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