Genus Two Generalization of A1 spherical Double Affine Hecke Algebra

Seminar: 
Geometry, Symmetry and Physics
Event time: 
Tuesday, March 27, 2018 - 4:30pm to 5:30pm
Speaker: 
Semen Artamonov
Speaker affiliation: 
Rutgers University
Event description: 

Spherical Double Affine Hecke Algebra can be viewed as a noncommutative (q,t)-deformation of the SL(N,C) character variety of the fundamental group of a torus. This deformation inherits major topological property from its commutative counterpart, namely Mapping Class Group of a torus SL(2,Z) acts by atomorphisms of DAHA. In my talk I will define a genus two analogue of A1 spherical DAHA and show thatthe Mapping Class Group of a closed genus two surface acts by automorphisms of such algebra. I will then show that for special values of parameters q,t satisfying qnt2=1 for some nonnegative integer n this algebra admits finite dimensional representations. I will conclude with discussion of potential applications to TQFT and knot theory.Based on arXiv:1704.02947 joint with Sh. Shakirov