On multiplicities of points on Schubert varieties in Graszmannians II

Details On multiplicities of points on Schubert varieties in Graszmannians II On multiplicities of points on Schubert varieties in Graszmannians II

2001-12-27

arxiv.org/abs/math/0112285v1

J. Algebraic Combin. 22 (2005), 273-288.

Mathematics

Algebraic Geometry

11 pages, AmS-TeX

Scientific paper

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 (S\'eminaire 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).

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