Séminaire Lotharingien de Combinatoire, 78B.77 (2017), 12 pp.

Gurbir Dhillon and Apoorva Khare

The Weyl-Kac Weight Formula

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.

Received: November 14, 2016. Accepted: February 17, 2017. Final version: April 1, 2017.

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