Quantum Toroidal and Shuffle Algebras

In this paper, we prove that the quantum toroidal algebra of type A is isomorphic to the double shuffle algebra of Feigin and Odesskii. The shuffle algebra viewpoint will allow us to prove a factorization formula for the universal R-matrix of the quantum toroidal algebra, and also prove a conjecture of Kuznetsov about the K-theory of affine Laumon spaces


Refined knot invariants and Hilbert schemes

Moduli of Flags of Sheaves and their K-theory