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October 2021 A local characterization of $B_{2}$ regular crystals
Shunsuke Tsuchioka
Proc. Japan Acad. Ser. A Math. Sci. 97(8): 51-56 (October 2021). DOI: 10.3792/pjaa.97.010

Abstract

Stembridge characterized regular crystals associated with a simply-laced generalized Cartan matrix (GCM) in terms of local graph-theoretic quantities. We give a similar axiomatization for $B_{2}$ regular crystals and thus for regular crystals associated with a finite GCM except $G_{2}$ and an affine GCM except $A^{(1)}_{1},G^{(1)}_{2},A^{(2)}_{2},D^{(3)}_{4}$.

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Shunsuke Tsuchioka. "A local characterization of $B_{2}$ regular crystals." Proc. Japan Acad. Ser. A Math. Sci. 97 (8) 51 - 56, October 2021. https://doi.org/10.3792/pjaa.97.010

Information

Published: October 2021
First available in Project Euclid: 1 October 2021

Digital Object Identifier: 10.3792/pjaa.97.010

Subjects:
Primary: 05E10 , 20G42

Keywords: Kashiwara crystals , local characterization , quantum groups

Rights: Copyright © 2021 The Japan Academy

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Vol.97 • No. 8 • October 2021
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