Primed decomposition tableaux and extended queer crystals

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. 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

References in corpus (7)

• K-theoretic analogues of factorial Schur P- and Q-functions
• Highest weight modules over quantum queer Lie superalgebra U_q(q(n))
• Characterization of queer supercrystals
• A local characterization of crystals for the quantum queer superalgebra
• $\mathfrak{q}$-crystal structure on primed tableaux and on signed unimodal factorizations of reduced words of type $B$
• Bumping operators and insertion algorithms for queer supercrystals
• Shifted insertion algorithms for primed words