Affine quantum Schur algebras and affine Hecke algebras
Qiang Fu

TL;DR
This paper extends the classification of finite dimensional irreducible modules for affine quantum Schur algebras and affine Hecke algebras, generalizing previous results to the case where the rank parameter n is less than or equal to r.
Contribution
It generalizes the determination of Drinfeld polynomials and classifies irreducible modules for affine quantum Schur algebras in the case n ≤ r, expanding prior work limited to n > r.
Findings
Generalized Drinfeld polynomial results to n ≤ r case
Classified finite dimensional irreducible modules for affine quantum Schur algebras
Extended classical results to the affine case
Abstract
Let be the Schur functor from the category of finite dimensional -modules to the category of finite dimensional -modules, where is the extended affine Hecke algebra of type over and is the affine quantum Schur algebras over . The Drinfeld polynomials associated with were determined in \cite[7.6]{CP96} and \cite[4.4.2]{DDF} in the case of , where is an irreducible -module. We will generalize the result in [loc. cit.] to the case of . As an application, we will classify finite dimensional irreducible -modules, which has been proved in…
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