Geometric lifting of the canonical basis and semitoric degenerations of Richardson varieties
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- by Sophie Morier-Genoud PDF
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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).References
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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
- Received by editor(s): April 26, 2005
- Received by editor(s) in revised form: September 27, 2005
- Published electronically: June 22, 2007
- © Copyright 2007
American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication. - Journal: Trans. Amer. Math. Soc. 360 (2008), 215-235
- MSC (2000): Primary 14M25, 16W35, 14M15
- DOI: https://doi.org/10.1090/S0002-9947-07-04216-X
- MathSciNet review: 2342001