# Mathematical Sciences Research Institute

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# Seminar

Combinatorics Seminar: Characterization of queer supercrystals February 25, 2019 (12:10 PM PST - 01:00 PM PST)
Parent Program: -- UC Berkeley Math (Evans Hall 939)
Speaker(s) Wencin Poh (University of California, Davis)
Description No Description
Video
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.