Small Representations for Affine q-Schur Algebras

TL;DR

This paper investigates the simple modules of affine q-Schur algebras, focusing on their associated Drinfeld polynomials, and provides explicit computations for modules derived from finite q-Schur algebra modules.

Contribution

It explicitly computes the Drinfeld polynomials for simple modules of affine q-Schur algebras obtained via evaluation from finite q-Schur algebra modules.

Findings

Explicit formulas for Drinfeld polynomials of certain simple modules

Connection between affine and finite q-Schur algebra modules

Advancement in understanding module classification in affine quantum groups

Abstract

When the parameter $q\in\mathbb C^*$ is not a root of unity, simple modules of affine $q$-Schur algebras have been classified in terms of Frenkel--Mukhin's dominant Drinfeld polynomials (\cite[4.6.8]{DDF}). We compute these Drinfeld polynomials associated with the simple modules of an affine $q$-Schur algebra which come from the simple modules of the corresponding $q$-Schur algebra via the evaluation maps.