Séminaire Lotharingien de Combinatoire, 93B.34 (2025), 12 pp.
Hyeonjae Choi, Donghyun Kim and Seung Jin Lee
Lusztig q-Weight Multiplicities and KR Crystals
Abstract.
Lusztig q-weight multiplicities extend the Kostka-Foulkes
polynomials to a broader range of Lie types.
In this work, we investigate these multiplicities through the
framework of Kirillov-Reshetikhin crystals.
Specifically, for type C and type B spin weights, we present a
combinatorial formula for Lusztig q-weight multiplicities in terms
of energy functions of Kirillov-Reshetikhin crystals, generalizing the
charge statistic on semistandard Young tableaux for type A.
Additionally, we introduce level-restricted q-weight multiplicities
for nonexceptional types, and prove its positivity by providing their
combinatorial formulas.
Received: November 15, 2024.
Accepted: February 15, 2025.
Final version: April 1, 2025.
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