Geometric lifting of the canonical basis and semitoric degenerations of Richardson varieties
Abstract
In the sl\n case, A. Berenstein and A. Zelevinsky studied the Sch\"utzenberger involution in terms of Lusztig's canonical basis, [3]. We generalize their construction and formulas for any semisimple Lie algebra. We use for this the geometric lifting of the canonical basis, on which an analogue of the Sch\"utzenberger involution can be given. As an application, we construct semitoric degenerations of Richardson varieties, following a method of P. Caldero, [6]
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