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

Watanabe, Hideya

doi:10.1090/ert/556

Global crystal bases for integrable modules over a quantum symmetric pair of type AIII
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Represent. Theory 25 (2021), 27-66 Request permission

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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