Demystifying the cocharacter sequences of upper triangular matrix algebras

Paper Title:

Cocharacters of $UT_n(E)$

Published on:

6 January 2023

Primary Category:

Rings and Algebras

Paper Authors:

Lucio Centrone,

Vesselin Drensky,

Daniela Martinez Correa

Bullets

Key Details

•

The authors calculate the generating function for the cocharacter sequence of the n x n upper triangular matrix algebra over the Grassmann algebra.

•

They define the (k,l)-multiplicity series of a PI-algebra, which captures multiplicities for partitions in a hook of height k and width l.

•

The double Hilbert series of the Grassmann algebra and the upper triangular matrix algebras are computed.

•

An algorithm is derived to determine the (k,l)-multiplicity series of the upper triangular matrix algebras, allowing computation of cocharacter multiplicities.

Explore the topics in this paper

double-hilbert-series

grassmann-algebras

infinite-dimensional-algebras

pi-algebras

upper-triangular-matrix-algebras

AI generated summary

Demystifying the cocharacter sequences of upper triangular matrix algebras

This paper studies the cocharacter sequences of upper triangular matrix algebras over the infinite dimensional Grassmann algebra. I summarized the key contributions as: calculating the generating function of the cocharacter sequence, defining the (k,l)-multiplicity series, computing the double Hilbert series, and deriving an algorithm to determine the (k,l)-multiplicity series.