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CATEGORIES:Algebra and Representation Theory Seminar
SUMMARY:Quantum character varieties and the double affine
Hecke algebra - David Jordan (Edinburgh)
DTSTART;TZID=Europe/London:20170125T163000
DTEND;TZID=Europe/London:20170125T173000
UID:TALK69246AThttp://talks.cam.ac.uk
URL:http://talks.cam.ac.uk/talk/index/69246
DESCRIPTION:The character variety of a manifold is a moduli sp
ace of representations of its fundamental group in
to some fixed gauge group. In this talk I will out
line the construction of a fully extended topologi
cal field theory in dimension 4\, which gives a un
iform functorial quantization of the character\nva
rieties of low-dimensional manifolds\, when the ga
uge group is reductivealgebraic (e.g. GL_N).\n\nI'
ll focus on important examples in representation t
heory arising from the construction\, in genus 1:
spherical double affine Hecke algebras (DAHA)\,\n
difference-operator deformations of the Grothendie
ck-Springer sheaf\, and the construction of irredu
cible DAHA modules. The general constructions are
\njoint with David Ben-Zvi and Adrien Brochier\, a
nd development of several of the examples are join
t with Martina Balagovic and Monica Vazirani.\n
LOCATION:MR12
CONTACT:Christopher Brookes
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