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Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)

 

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


Author: Sophie Morier-Genoud
Journal: Trans. Amer. Math. Soc. 360 (2008), 215-235
MSC (2000): Primary 14M25, 16W35, 14M15
Published electronically: June 22, 2007
MathSciNet review: 2342001
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Abstract: 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).


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Additional Information

Sophie Morier-Genoud
Affiliation: Département de Mathématiques, Université Claude Bernard Lyon I, 69622 Villeurbanne Cedex, France
Email: morier@math.univ-lyon1.fr

DOI: http://dx.doi.org/10.1090/S0002-9947-07-04216-X
PII: S 0002-9947(07)04216-X
Received by editor(s): April 26, 2005
Received by editor(s) in revised form: September 27, 2005
Published electronically: June 22, 2007
Article copyright: © Copyright 2007 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.