Small Representations for Affine q-Schur Algebras
Jie Du, Qiang Fu

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 is not a root of unity, simple modules of affine -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 -Schur algebra which come from the simple modules of the corresponding -Schur algebra via the evaluation maps.
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Taxonomy
TopicsAlgebraic structures and combinatorial models · Nonlinear Waves and Solitons · Advanced Combinatorial Mathematics
