Quantum character varieties and the double affine Hecke algebra

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• David Jordan (Edinburgh)
• Wednesday 25 January 2017, 16:30-17:30
• MR12.

If you have a question about this talk, please contact Christopher Brookes.

The character variety of a manifold is a moduli space of representations of its fundamental group into some fixed gauge group. In this talk I will outline the construction of a fully extended topological field theory in dimension 4, which gives a uniform functorial quantization of the character varieties of low-dimensional manifolds, when the gauge group is reductivealgebraic (e.g. GL_N).

I’ll focus on important examples in representation theory arising from the construction, in genus 1: spherical double affine Hecke algebras (DAHA), difference-operator deformations of the Grothendieck-Springer sheaf, and the construction of irreducible DAHA modules. The general constructions are joint with David Ben-Zvi and Adrien Brochier, and development of several of the examples are joint with Martina Balagovic and Monica Vazirani.

This talk is part of the Algebra and Representation Theory Seminar series.

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