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The Affineq-Schur Algebra

✍ Scribed by R.M Green

Publisher
Elsevier Science
Year
1999
Tongue
English
Weight
202 KB
Volume
215
Category
Article
ISSN
0021-8693

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✦ Synopsis

We introduce an analogue of the q-Schur algebra associated to Coxeter systems Γ΄f type A

. We give two constructions of this algebra. The first construction ny 1

realizes the algebra as a certain endomorphism algebra arising from an affine Δ€ecke algebra of type A , where n G r. This generalizes the original q-Schur ry 1 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 Ε½ . q-Schur algebra as a quotient of U α’„ α’‰ .

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