A geometric construction of generalized q-Schur algebras

Abstract

We show that the algebras constructed in [Li10] and [Li12] are generalized q-Schur algebras as defined in [D03]. This provides a geometric construction of generalized q-Schur algebras in types A, D and E. We give a parameterization of Nakajima's Lagrangian quiver variety of type D associated to a certain highest weight.

Typos corrected. Final version. To appear in the Proceedings of the AMS Special Sessions on Geometric and Algebraic Aspects of Representation Theory and Quantum Groups and Noncommutative Algebraic Geometry