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Global crystal bases for integrable modules over a quantum symmetric pair of type AIII


Author: Hideya Watanabe
Journal: Represent. Theory 25 (2021), 27-66
MSC (2020): Primary 17B10
DOI: https://doi.org/10.1090/ert/556
Published electronically: January 12, 2021
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Abstract: In this paper, we study basic properties of global $ \jmath $-crystal bases for integrable modules over a quantum symmetric pair coideal subalgebra $ \mathbf {U}^{\jmath }$ associated to the Satake diagram of type AIII without black nodes. Also, we obtain an intrinsic characterization of the $ \jmath $-crystal bases, whose original definition is artificial.


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Additional Information

Hideya Watanabe
Affiliation: Research Institute for Mathematical Sciences, Kyoto University, Kyoto 606-8052, Japan
Email: hideya@kurims.kyoto-u.ac.jp

DOI: https://doi.org/10.1090/ert/556
Keywords: Quantum symmetric pair, Hecke algebra, global crystal basis
Received by editor(s): November 16, 2019
Received by editor(s) in revised form: September 21, 2020
Published electronically: January 12, 2021
Additional Notes: This work was supported by JSPS KAKENHI grant number 17J00172
Article copyright: © Copyright 2021 American Mathematical Society