The Weyl-Kac weight formula
Representation Theory
2018-02-21 v1 Combinatorics
Quantum Algebra
Abstract
We provide the first formulae for the weights of all simple highest weight modules over Kac-Moody algebras. For generic highest weights, we present a formula for the weights of simple modules similar to the Weyl-Kac character formula. For the remaining highest weights, the formula fails in a striking way, suggesting the existence of 'multiplicity-free' Macdonald identities for affine root systems.
Cite
@article{arxiv.1802.06974,
title = {The Weyl-Kac weight formula},
author = {Gurbir Dhillon and Apoorva Khare},
journal= {arXiv preprint arXiv:1802.06974},
year = {2018}
}
Comments
12 pages, final version. This is an extended abstract of arXiv:1606.09640 in FPSAC 2017