THE AFFINE q - SCHUR ALGEBRAR
نویسنده
چکیده
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 q-Schur algebra and the aane Hecke algebra as subalgebras. Using this approach we can prove a double centralizer property. The second construction realizes the aane 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
Structures and Representations of Affine q-Schur Algebras
This paper provides a survey for the latest developments in the theory of affine q-Schur algebras and Schur–Weyl duality between affine quantum gln and affine type A Hecke algebras. More precisely, we will establish, on the one side, an isomorphism between the double Ringel–Hall algebra D△(n) of a cyclic quiver △(n) and the quantum loop algebra of gln, and establish, on the other side, explicit...
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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 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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