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

Watanabe, Hideya

doi:10.1090/ert/556

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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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