Symmetrizable Quantum Affine Superalgebras And Their Representations

Abstract

Aspects of the algebraic structure and representation theory of the quantum affine superalgebras with symmetrizable Cartan matrices are studied. The irreducible integrable highest weight representations are classified, and shown to be deformations of their classical counterparts. It is also shown that Jimbo type quantum affine superalgebras can be obtained by deforming universal enveloping algebras of ordinary (i.e., non-graded) affine algebras supplemented by certain parity operators.Comment: Latex, 14 page