Quantum D-Modules

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• Nicolas Dupré, University of Cambridge
• Friday 29 May 2015, 15:00-16:00
• CMS, MR14.

If you have a question about this talk, please contact Julian Brough.

In their 2006 paper, Backelin and Kremnizer developed a theory of quantum D-modules. There had been several earlier attempts at defining quantum D-modules (e.g. by Tanisaki), but they were all trying to define an algebra of quantum differential operators on G/N, which lead to difficulties. The approach taken by Backelin and Kremnizer was to use the language of equivariant sheaves, which allowed them to write all the classical definitions they needed in terms of affine varieties, i.e. purely in terms of algebras. For instance, this allowed them to define a notion of quantum flag variety. My aim is to explain their theory of quantum D-modules, leading to a quantum analogue of the Beilinson-Bernstein theorem. I will not assume any previous knowledge of quantum groups. Time permitting, I will also say something about how one might try to define quantum p-adic groups.

This talk is part of the Junior Algebra and Number Theory seminar series.

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