Séminaire Lotharingien de Combinatoire, 91B.62 (2024), 12 pp.
Taehyeok Heo
Extremal Weight Crystals over Affine Lie Algebras of Infinite Rank
Abstract.
We explain extremal weight crystals over affine Lie algebras of infinite rank using combinatorial models:
a spinor model due to Kwon, and an infinite rank analogue of Kashiwara-Nakashima tableaux due to Lecouvey.
In particular, we show that the Lecouvey's tableau model combinatorially explains an extremal weight crystal structure of level zero.
Using these combinatorial models, we explain an algebra structure of the Grothendieck ring for a category consisting of some extremal weight crystals.
Received: November 15, 2023.
Accepted: February 15, 2024.
Final version: April 1, 2024.
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