Séminaire Lotharingien de Combinatoire, 91B.73 (2024), 12 pp.
Eric Marberg and Kam Hung Tong
Crystals for Variations of Decomposition Tableaux
Abstract.
Our previous work introduced a category of extended queer crystals, whose connected normal objects have unique highest weight elements and characters that are Schur Q-polynomials. Our initial models for such crystals were based on semistandard shifted tableaux. Here, we introduce a simpler construction using certain "primed" decomposition tableaux, which slightly generalize the decomposition tableaux used in work of Grantcharov et al. This leads to a new, much shorter proof of the highest weight properties of the normal subcategory of extended queer crystals. We also describe a natural crystal structure on set-valued decomposition tableaux. Our results give the first crystal constructions for shifted set-valued tableaux, and lead to partial progress on a conjectural formula of Cho and Ikeda for K-theoretic Schur P-functions.
Received: November 15, 2023.
Accepted: February 15, 2024.
Final version: April 1, 2024.
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