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

Abstract

In this paper, we study basic properties of global $ȷ$-crystal bases for integrable modules over a quantum symmetric pair coideal subalgebra ${\mathbf{U}}^{ȷ}$ associated to the Satake diagram of type AIII with even white nodes and no black nodes. Also, we obtain an intrinsic characterization of the $ȷ$-crystal bases, whose original definition is artificial.

34 pages, minor corrections