Geometric lifting of the canonical basis and semitoric degenerations of Richardson varieties

Sophie Morier-Genoud (1)

1 ICJ - Institut Camille Jordan

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]

Mots clés: canonical basis; Richardson varieties; geometric lifting; toric degeneration; tropicalization

Domaines: Théorie des représentations [math.RT]; Géométrie algébrique [math.AG]

Sophie Morier-Genoud. Geometric lifting of the canonical basis and semitoric degenerations of Richardson varieties. 2005. ⟨hal-00004804v3⟩