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The Weyl-Kac weight formula

Published 20 Feb 2018 in math.RT, math.CO, and math.QA | (1802.06974v1)

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.

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