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We describe the implementation of queer supercrystals. Our code is docu- mented with test suites and has been integrated into SageMath. Through computer explorations using this implementation, we provide a counterexample to Assaf’s and Oguz’ conjecture that their local queer axioms uniquely characterize the queer super- crystal.
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Combinatorial Characterization of Queer Supercrystals (Survey)
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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- PAR ID:
- 10287087
- Date Published:
- Journal Name:
- Advances in mathematical sciences
- Volume:
- 21
- ISSN:
- 2664-598X
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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- Free Publicly Accessible Full Text
-
Accepted Manuscript1.0
- Journal Article:
- https://doi.org/10.1007/978-3-030-42687-3_4
