科研之友
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摘要
We formulate a q-Schur algebra associated with an arbitrary W-invariant finite set X-f of integral weights for a complex simple Lie algebra with Weyl group W. We establish a q-Schur duality between the q-Schur algebra and Hecke algebra associated with W. We then realize geometrically the q-Schur algebra and duality and construct a canonical basis for the q-Schur algebra with positivity. With suitable choices of X-f in classical types, we recover the q-Schur algebras in the literature. Our q-Schur algebras are closely related to the category O, where the type G(2) is studied in detail.
