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arXiv · 1809.04647

Characterization of queer supercrystals

Maria Gillespie·Graham Hawkes·Wencin Poh·Anne Schilling
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Abstract

We provide a characterization of the crystal bases for the quantum queer superalgebra recently introduced by Grantcharov et al.. This characterization is a combination of local queer axioms generalizing Stembridge's local axioms for crystal bases for simply-laced root systems, which were recently introduced by Assaf and Oguz, with further axioms and a new graph $G$ characterizing the relations of the type $A$ components of the queer crystal. We provide a counterexample to Assaf's and Oguz' conjecture that the local queer axioms uniquely characterize the queer supercrystal. We obtain a combinatorial description of the graph $G$ on the type $A$ components by providing explicit combinatorial rules for the odd queer operators on certain highest weight elements.

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BibTeXRIS

Maria Gillespie, Graham Hawkes, Wencin Poh, Anne Schilling. 2018-09-12. Characterization of queer supercrystals. https://doi.org/10.1016/j.jcta.2020.105235

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