Quantum Toroidal Superalgebras

2020-04-30T16:04:11Z (GMT) by Luan Pereira Bezerra
We introduce the quantum toroidal superalgebra Em|n associated with the Lie superalgebra glm|n and initiate its study. For each choice of parity "s" of glm|n, a corresponding quantum toroidal superalgebra Es is defined.

To show that all such superalgebras are isomorphic, an action of the toroidal braid group is constructed.

The superalgebra Es contains two distinguished subalgebras, both isomorphic to the quantum affine superalgebra Uq sl̂m|n with parity "s", called vertical and horizontal subalgebras. We show the existence of Miki automorphism of Es, which exchanges the vertical and horizontal subalgebras.

If m and n are different and "s" is standard, we give a construction of level 1 Em|n-modules through vertex operators. We also construct an evaluation map from Em|n(q1,q2,q3) to the quantum affine algebra Uq gl̂m|n at level c=q3(m-n)/2.