Quantum Toroidal Superalgebras

Luan Pereira Bezerra, Purdue University

Abstract

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 Esis defined. To show that all such superalgebras are isomorphic, an action of the toroidal braid group Bbm+n on the direct sum ⊕sEsis constructed. The superalgebra Es contains two distinguished subalgebras, both isomorphic to the quantum affine superalgebra Uqslbm: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. For m =n and standard parity, 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 Uqglb m:n at level c = q 3(m−n)/2 .

Degree

Ph.D.

Advisors

Mukhin, Purdue University.

Subject Area

Mathematics

COinS