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

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

2005-04-26

arxiv.org/abs/math/0504538v3

Mathematics

Representation Theory

22 pages, 3 figures

Scientific paper

In the sl\_n case, A. Berenstein and A. Zelevinsky studied the Sch\"{u}tzenberger 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\"{u}tzenberger 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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