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- W2036416325 abstract "We introduce an analogue of the $q$-Schur algebra associated to Coxeter systems of type $hat A_{n-1}$. We give two constructions of this algebra. The first construction realizes the algebra as a certain endomorphism algebra arising from an affine Hecke algebra of type $hat A_{r-1}$, where $n geq r$. This generalizes the original $q$-Schur algebra as defined by Dipper and James, and the new algebra contains the ordinary $q$-Schur algebra and the affine Hecke algebra as subalgebras. Using this approach we can prove a double centralizer property. The second construction realizes the affine $q$-Schur algebra as the faithful quotient of the action of a quantum group on the tensor power of a certain module, analogous to the construction of the ordinary $q$-Schur algebra as a quotient of $U(frak g frak l_n)$." @default.
- W2036416325 created "2016-06-24" @default.
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- W2036416325 date "1997-05-23" @default.
- W2036416325 modified "2023-09-27" @default.
- W2036416325 title "The Affine q-Schur algebra" @default.
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