On multiplicities of points on Schubert varieties in Grassmannians

Details On multiplicities of points on Schubert varieties in Grassmannians On multiplicities of points on Schubert varieties in Grassmannians

2000-11-17

arxiv.org/abs/math/0011129v1

S\'eminaire Lotharingien Combin. 45 (2001), Article B45c, 11 pp

Mathematics

Algebraic Geometry

10 pages, AmS-TeX

Scientific paper

We answer some questions related to multiplicity formulas by Rosenthal and Zelevinsky and by Lakshmibai and Weyman for points on Schubert varieties in Grassmannians. In particular, we give combinatorial interpretations in terms of nonintersecting lattice paths of these formulas, which makes the equality of the two formulas immediately obvious. Furthermore we provide an alternative determinantal formula for these multiplicities, and we show that they count semistandard tableaux of unusual shapes.

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