Finite-dimensional representations of map superalgebras

Abstract

We describe the block decomposition of the categories of finite-dimensional modules for classical map superalgebras and affine superalgebras in terms of spectral characters. En route to showing these block decompositions, we obtain a new description of finite-dimensional irreducible modules for classical map and affine superalgebras, provide formulas for their (super)characters and describe their extension groups. As an application, we establish a relation between the highest weights of a given finite-dimensional irreducible module for a classical map superalgebra with respect to non-conjugate Borel subalgebras.