Fall 2014

Characters of Equivariant D-modules on Veronese Cones

Monday, November 10th, 2014 2:30 pm3:20 pm

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Equivariant local systems on orbits of a group action give rise via the Riemann-Hilbert correspondence to equivariant D-modules, which are typically hard to describe. I will explain how to compute explicitly the characters of the GL-equivariant D-modules supported on the Veronese cones. In particular, I will appeal to recent results of de Cataldo, Migliorini and Mustaţă on the Decomposition Theorem for toric maps, and show how representation theoretic stabilization results are used in a crucial way in the calculation. As an application, I'll show that the local cohomology with support on a Veronese cone is a simple equivariant D-module.