Cocharacters of $UT_n(E)$

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 U Tn(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 U Tn(E).