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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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