Finite-dimensional representations of map superalgebras
Representation Theory
2021-05-17 v1
Abstract
We obtain a complete classification of all finite-dimensional irreducible modules over classical map superalgebras, provide formulas for their (super)characters and a description of their extension groups. Furthermore, we describe the block decomposition of the category of finite-dimensional modules for such map superalgebras. As an application, we specialize our results to the case of loop superalgebras in order to obtain a classification of finite-dimensional irreducible modules and block decomposition of the category of finite-dimensional modules over affine Lie superalgebras.
Keywords
Cite
@article{arxiv.2105.06994,
title = {Finite-dimensional representations of map superalgebras},
author = {Lucas Calixto and Tiago Macedo},
journal= {arXiv preprint arXiv:2105.06994},
year = {2021}
}