The affine q-Schur algebra.

Green, R. M. (1999) The affine q-Schur algebra. Journal of Algebra, 215 (2). pp. 379-411. ISSN 0021-8693

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Abstract

We introduce an analogue of theq-Schur algebra associated to Coxeter systems of typeÁn − 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 typeÁr − 1, wheren ≥ r. This generalizes the originalq-Schur algebra as defined by Dipper and James, and the new algebra contains the ordinaryq-Schur algebra and the affine Hecke algebra as subalgebras. Using this approach we can prove a double centralizer property. The second construction realizes the affineq-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 ordinaryq-Schur algebra as a quotient ofU( n).

Item Type:
Journal Article
Journal or Publication Title:
Journal of Algebra
Uncontrolled Keywords:
/dk/atira/pure/researchoutput/libraryofcongress/qa
Subjects:
ID Code:
19393
Deposited By:
Deposited On:
14 Nov 2008 10:01
Refereed?:
Yes
Published?:
Published
Last Modified:
07 Jan 2020 02:27