The Weyl-Kac weight formula
Gurbir Dhillon, Apoorva Khare
TL;DR
This paper introduces the first explicit formulas for weights of all simple highest weight modules over Kac-Moody algebras, revealing new phenomena for special weights and suggesting novel identities for affine root systems.
Contribution
It provides the first comprehensive weight formulas for simple modules over Kac-Moody algebras, including cases where previous formulas fail, indicating new algebraic identities.
Findings
Formulas for weights of all simple highest weight modules
Failure of formulas for certain special weights
Indication of 'multiplicity-free' Macdonald identities
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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Taxonomy
TopicsAlgebraic structures and combinatorial models · Advanced Combinatorial Mathematics · Advanced Algebra and Geometry