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

In the \mathfrak{sl}_n case, A. Berenstein and A. Zelevinsky (1996) studied the Schützenberger involution in terms of Lusztig's canonical basis. We generalize their construction and formulas for any semisimple Lie algebra. We use the geometric lifting of the canonical basis, on which an analogu...

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Bibliographic Details
Published in:Transactions of the American Mathematical Society 2008-01, Vol.360 (1), p.215-235
Main Author: Sophie Morier-Genoud
Format: Article
Language:English
Subjects:
Algebra
Automorphisms
Combinatorics
Coordinate systems
Exact sciences and technology
Functional analysis
Mathematical analysis
Mathematical theorems
Mathematical vectors
Mathematics
Nonassociative rings and algebras
Polytopes
Rhytidoplasty
Sciences and techniques of general use
Tableaux
Vertices
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Summary:In the \mathfrak{sl}_n case, A. Berenstein and A. Zelevinsky (1996) studied the Schützenberger involution in terms of Lusztig's canonical basis. We generalize their construction and formulas for any semisimple Lie algebra. We use 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 (2002).
ISSN:0002-9947
1088-6850
DOI:10.1090/S0002-9947-07-04216-X