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Séminaire Lotharingien de Combinatoire, B45c (2001), 11 pp.

# Christian Krattenthaler

#
On Multiplicities of Points on Schubert Varieties in
Grassmannians

**Abstract.**
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.

Received: December 12, 2000; Accepted: January 16, 2001.

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