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arXiv · 1803.06317

A local characterization of crystals for the quantum queer superalgebra

Sami Assaf·Ezgi Kantarci Oguz
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Abstract

We define operators on semistandard shifted tableaux and use Stembridge's local characterization for regular graphs to prove they define a crystal structure. This gives a new proof that Schur $P$-polynomials are Schur positive. We define queer crystal operators (also called odd Kashiwara operators) to construct a connected queer crystal on semistandard shifted tableaux of a given shape. Using the tensor rule for queer crystals, this provides a new proof that products of Schur $P$-polynomials are Schur $P$-positive. Finally, to facilitate applications of queer crystals in the context of Schur $P$-positivity, we give local axioms for queer regular graphs, generalizing Stembridge's axioms, that partially characterize queer crystals.

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BibTeXRIS

Sami Assaf, Ezgi Kantarci Oguz. 2018-03-16. A local characterization of crystals for the quantum queer superalgebra. https://doi.org/10.1007/s00026-019-00477-0

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