On multiplicities of points on Schubert varieties in Graszmannians II

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We prove a conjecture by Kreiman and Lakshmibai on a combinatorial description of multiplicities of points on Schubert varieties in Graszmannians in terms of certain sets of reflections in the corresponding Weyl group. The proof is accomplished by setting up a bijection between these sets of reflections and the author's previous combinatorial interpretation of these multiplicities in terms of nonintersecting lattice paths (Séminaire Lotharingien Combin. 45 (2001), Article B45c; see http://www.mat.univie.ac.at/~slc/wpapers/s45kratt.html or http://www.arxiv.org/abs/math.AG/0011129).
11 pages, AmS-TeX

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Algebraic Geometry, Commutative Algebra, Combinatorics, Rings and Algebras, 14M15 (Primary) 05A15 05E15 14H20 (Secondary)

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http://salesiana.dossiersoluciones.com/handle/123456789/96011

Consulte el texto completo en el siguiente enlace:

https://arxiv.org/abs/math/0112285
 http://arxiv.org/abs/math/0112285
 J. Algebraic Combin. 22 (2005), 273-288.

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arXiv