Braid actions on quantum toroidal superalgebras

Abstract

We prove that the quantum toroidal algebras ${\mathcal{E}}_{\mathbf{s}}$ associated with different root systems $\mathbf{s}$ of ${\mathfrak{gl}}_{m|n}$ type are isomorphic. We also show the existence of Miki automorphism of ${\mathcal{E}}_{\mathbf{s}}$, which exchanges the vertical and horizontal subalgebras. To obtain these results, we establish an action of the toroidal braid group on the direct sum ${\oplus }_{\mathbf{s}}{\mathcal{E}}_{\mathbf{s}}$ of all such algebras.

v1: LaTex, 25 pages. v2: minor corrections

References in corpus (1)

• Shuffle algebra realizations of type $A$ super Yangians and quantum affine superalgebras for all Cartan data

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