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Geometric lifting of the canonical basis and semitoric degenerations of Richardson varieties
Sophie Morier-Genoud1

In the sl_n case, A. Berenstein and A. Zelevinsky studied the Schützenberger 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 Schützenberger involution can be given. As an application, we construct semitoric degenerations of Richardson varieties, following a method of P. Caldero, [6]
1:  ICJ - Institut Camille Jordan
canonical basis – Richardson varieties – geometric lifting – toric degeneration – tropicalization