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.

The following versions are available: