Braid actions on quantum toroidal superalgebras

Abstract

We prove that the quantum toroidal algebras Es associated with different root systems s of glm|n type are isomorphic. We also show the existence of Miki automorphism of Es, which exchanges the vertical and horizontal subalgebras. To obtain these results, we establish an action of the toroidal braid group on the direct sum ⊕sEs of all such algebras.