Fusion procedure for the walled Brauer algebra

TL;DR

This paper develops two fusion procedures for the walled Brauer algebra, constructing primitive orthogonal idempotents via evaluations of rational functions on standard walled tableaux, advancing algebraic representation theory.

Contribution

It introduces two novel fusion procedures for the walled Brauer algebra, enabling explicit construction of primitive orthogonal idempotents through rational function evaluations.

Findings

Constructed complete systems of primitive orthogonal idempotents.

Established two versions of the fusion procedure.

Connected evaluations on standard walled tableaux to algebraic structures.

Abstract

We establish two versions of the fusion procedure for the walled Brauer algebras. In each of them, a complete system of primitive pairwise orthogonal idempotents for the walled Hecke algebra is constructed by consecutive evaluations of a rational function in several variables on contents of standard walled tableaux.