<p>Our previous work introduced a category of extended queer crystals, whose connected normal objects have unique highest weight elements and characters that are Schur <i>Q</i>-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.</p>

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Primed Decomposition Tableaux and Extended Queer Crystals

  • Eric Marberg,
  • Kam Hung Tong

摘要

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.