This material has been published in
J. Algebraic Combin. 22 (2005), 273-288,
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Christian Krattenthaler
On multiplicities of points on Schubert varieties in
Graßmannians
(16 pages)
Abstract.
We prove a conjecture by Kreiman and Lakshmibai on a combinatorial
description of multiplicities of points on Schubert
varieties in Graßmannians 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.
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