Anton Mellit – A_{q,t} algebra as a partially symmetrized DAHA and computations of knot invariants

The A_{q,t} algebra arose from my work with Erik Carlsson on the shuffle conjecture. I will explain how this algebra can be constructed naturally from a topological (skein-theoretic) point of view. Similarly to the way representation theory of quantum groups gl_N can be interpolated in the limit as N goes to infinity, the A_{q,t} algebra arises if one attempts to interpolate the symmetric power of the standard representation Sym_M in the limit as M goes to infinity. Then I will show how the algebra was used to compute the triply graded homology (superpolynomials) of torus knots.

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