v 2 1 3 O ct 1 99 8 THE AFFINE q - SCHUR ALGEBRA
نویسنده
چکیده
We introduce an analogue of the q-Schur algebra associated to Coxeter systems of type 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 A r−1 , where n ≥ 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 ten-sor power of a certain module, analogous to the construction of the ordinary q-Schur algebra as a quotient of U(gl n).
منابع مشابه
Presenting affine q-Schur algebras
We obtain a presentation of certain affine q-Schur algebras in terms of generators and relations. The presentation is obtained by adding more relations to the usual presentation of the quantized enveloping algebra of type affine gln. Our results extend and rely on the corresponding result for the q-Schur algebra of the symmetric group, which were proved by the first author and Giaquinto. Mathem...
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We obtain a presentation of certain affine q-Schur algebras in terms of generators and relations. The presentation is obtained by adding more relations to the usual presentation of the quantized enveloping algebra of type affine gl n. Our results extend and rely on the corresponding result for the q-Schur algebra of the symmetric group, which were proved by the first author and Giaquinto.
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متن کاملTHE AFFINE q - SCHUR ALGEBRAR
We introduce an analogue of the q-Schur algebra associated to Coxeter systems of type b A n?1. We give two constructions of this algebra. The rst construction realizes the algebra as a certain endomorphism algebra arising from an aane Hecke algebra of type b A r?1 , where n r. This generalizes the original q-Schur algebra as deened by Dipper and James, and the new algebra contains the ordinary ...
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