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Twisting the quantum Grassmannian

By Stephane Launois and T.H. Lenagan

Abstract

In contrast to the classical and semiclassical settings, the Coxeter element (12...n) which cycles the columns of an m x n matrix does not determine an automorphism of the quantum grassmannian. Here, we show that this cycling can be obtained by means of a cocycle twist. A consequence is that the torus invariant prime ideals of the quantum grassmannian are permuted by the action of the Coxeter element (12...n). We view this as a quantum analogue of the recent result of Knutson, Lam and Speyer, where the Lusztig strata of the classical grassmannian are permuted by (12...n)

Topics: QA150
Year: 2011
OAI identifier: oai:kar.kent.ac.uk:26027
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