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

2005/04/26 by Sophie Morier-Genoud, Morier-Genoud, Sophie
Mathematics · Physics and Astronomy · #14M15 #16W35 #Advanced Algebra and Geometry #Advanced Topics in Algebra #Algebraic Geometry (math.AG) #FOS: Mathematics #MSC: 14M25 #Nonlinear Waves and Solitons #Representation Theory (math.RT) #math.AG #math.RT #msc:14M15 #msc:14M25 #msc:16W35

paper · pdf · doi:10.48550/arxiv.math/0504538

22 pages, 3 figures

openalex publication_date 2005/04/26 · arxiv created 2005/10/19 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

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]

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