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Graduate Algebra and Representation Theory Seminar

Genus Two analogue of A_1 spherical DAHA

Semeon Artamonov, Rutgers University

Location:  Hill 525
Date & time: Monday, 09 October 2017 at 12:00PM - 1:00PM

Abstract: I will start by reviewing on how A_{n-1} spherical DAHA arise in the quantization of 
the moduli space of SU(N) flat connections on a torus. I will then define the corresponding 
notion for the case of SU(2) flat connections on a genus two surface. In particular, I will 
define a family of Laurent polynomials which form a basis of common eigenfunctions of certain 
commuting q-difference operators. This family contains A_1 Macdonald polynomials as a subclass. 

I will then define a genus two analogue of A_1 spherical DAHA and show that the Mapping Class 
Group of a genus two surface acts by outer automorphisms of this algebra.

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