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 Lecouvey’s tableau model is isomorphic to an extremal weight crystal 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.
Authors
- Taehyeok Heo (ORCID: https://orcid.org/0000-0002-1557-0124)
Institutions
- Seoul National University (KR)
Publication Details
- Journal
- Algebras and Representation Theory
- Published
- 2024-12-21
- DOI
- https://doi.org/10.1007/s10468-024-10302-9
- Primary Topic
- Algebraic structures and combinatorial models
- Type
- article
- Field-Weighted Citation Impact
- 0.00
Funders
- National Research Foundation
- Seoul National University
- National Research Foundation of Korea