Functions on Type A Nilpotent Orbit Covers

Alberto Malaney (University of Glasgow)

Wednesday 16th September 16:00-17:00
Maths 311B

Abstract

We use an analogue of the Springer resolution to describe the G-module structure on the ring R of regular functions on the universal cover of any nilpotent orbit for G = SL_n. Building on previous work on the extended Springer resolution, we construct a variety that is finite over the cotangent bundle of a partial flag variety G/P, and proper and birational over the affinization of the orbit cover. We use techniques in birational geometry to show that this variety has rational singularities, which provides us with the necessary cohomology vanishing results to describe R as an induced representation from a Levi subgroup of G. We will also describe the graded structure of R, as well as a minimal set of representations which generate it as a ring. This is joint work with William Graham and Scott Larson.

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