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SUMMARY:Quantum character varieties and the double affine Hecke algebra - 
 David Jordan (Edinburgh)
DTSTART:20170125T163000Z
DTEND:20170125T173000Z
UID:TALK69246@talks.cam.ac.uk
CONTACT:Christopher Brookes
DESCRIPTION:The character variety of a manifold is a moduli space of repre
 sentations of its fundamental group into some fixed gauge group. In this t
 alk I will outline the construction of a fully extended topological field 
 theory in dimension 4\, which gives a uniform functorial quantization of t
 he character\nvarieties of low-dimensional manifolds\, when the gauge grou
 p is reductivealgebraic (e.g. GL_N).\n\nI'll focus on important examples i
 n representation theory arising from the construction\, in genus 1:  spher
 ical double affine Hecke algebras (DAHA)\,\ndifference-operator deformatio
 ns of the Grothendieck-Springer sheaf\, and the construction of irreducibl
 e DAHA modules.  The general constructions are\njoint with David Ben-Zvi a
 nd Adrien Brochier\, and development of several of the examples are joint 
 with Martina Balagovic and Monica Vazirani.\n
LOCATION:MR12
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