On Grothendieck ring of the sequence of walled Brauer algebras

TL;DR

This paper introduces a diagrammatic method to analyze the Grothendieck ring of walled Brauer algebras, enabling explicit computation of structure constants and branching rules for cell modules.

Contribution

It provides a novel diagrammatic approach to study the Grothendieck ring and branching rules for a sequence of walled Brauer algebras, including calculation of structure constants.

Findings

Diagrammatic approach to branching rules

Explicit calculation of structure constants

Enhanced understanding of the Grothendieck ring structure

Abstract

In this paper, we provide a diagrammatic approach to study the branching rules for cell modules on a sequence of walled Brauer algebras. This also allows us to calculate the structure constants of multiplication over the Grothendieck ring of the sequence.