On multiplicities of points on Schubert varieties in Grassmannians. II
Journal of Algebraic Combinatorics, Tome 22 (2005) no. 3, pp. 273-288.

Voir la notice de l'article dans Electronic Library of Mathematics

Summary: We prove a conjecture by Kreiman and Lakshmibai on a combinatorial description of multiplicities of points on Schubert varieties in Graßmannian in terms of certain sets of reflections in the corresponding Weyl group. The proof is accomplished by relating these sets of reflections to the author's previous combinatorial interpretation of these multiplicities in terms of non-intersecting lattice paths (Séminaire Lotharingien Combin. 45 (2001), Article B45c). Moreover, we provide a compact formula for the Hilbert series of the tangent cone to a Schubert variety in a Graßmannian assuming the truth of another conjecture of Kreiman and Lakshmibai.
Mots-clés : keywords Schubert varieties, singularities, multiplicities, non-intersecting lattice paths, turns of paths 
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     title = {On multiplicities of points on {Schubert} varieties in {Grassmannians.} {II}},
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Krattenthaler, Christian F. On multiplicities of points on Schubert varieties in Grassmannians. II. Journal of Algebraic Combinatorics, Tome 22 (2005) no. 3, pp. 273-288. https://geodesic-test.mathdoc.fr/item/JAC_2005__22_3_a5/