Primed decomposition tableaux and extended queer crystals
arXiv:2312.15409 · doi:10.1007/s10468-025-10323-y
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 -polynomials. The 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, shorter proof of the highest weight properties of the normal subcategory of extended queer crystals. Along the way, we analyze a primed extension of Grantcharov et al.'s insertion scheme for decomposition tableaux.
43 pages, 3 figures; v2: minor corrections, added exposition, new Section 3.6; v3: major revision to Section 3.6, incorporating missing references and adding new results on shifted plactic relations; v4: minor corrections, final version