报告摘要：
| We formulate a q-Schur algebra associated to 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 to 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. This is joint work with Weiqiang Wang.
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