Quantum Toroidal Algebra Associated with glm|n

Abstract

We introduce and study the quantum toroidal algebra Em|n(q1,q2,q3) associated with the superalgebra glm|n with m≠n, where the parameters satisfy q1q2q3 = 1. We give an evaluation map. The evaluation map is a surjective homomorphism of algebras Em|n(q1,q2,q3)→U˜qglˆm|n to the quantum affine algebra associated with the superalgebra glm|n at level c completed with respect to the homogeneous grading, where q2 = q2 and qm−n3=c2. We also give a bosonic realization of level one Em|n(q1,q2,q3)-modules.