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JOURNAL OF
ALGEBRAIC
COMBINATORICS

  Editors-in-chief: C. A. Athanasiadis, T. Lam, A. Munemasa, H. Van Maldeghem
ISSN 0925-9899 (print) • ISSN 1572-9192 (electronic)
 

Multiplicities of Points on Schubert Varieties in Grassmannians

Joachim Rosenthal and Andrei Zelevinsky

DOI: 10.1023/A:1011253800374

Abstract

We obtain an explicit determinantal formula for the multiplicity of any point on a classical Schubert variety.

Pages: 213–218

Keywords: Schubert varieties; singularities; multiplicities; partial difference equation

Full Text: PDF

References

1. I. Gessel and G.X. Viennot, “Binomial determinants, paths, and hooklength formulae,” Adv. Math. 58 (1985), 300-321.
2. V. Lakshmibai, “Multiplicities of points on a Schubert variety,” C. R. Acad. Sci. Paris Sér. I Math. 321(2), (1995), 215-218.
3. V. Lakshmibai and J. Weyman, “Multiplicities of points on a Schubert variety in a minuscule G/P,” Adv. Math. 84 (1990), 179-208.
4. I.G. Macdonald, Symmetric Functions and Hall Polynomials, 2nd edition, Clarendon Press, Oxford, 1995.
5. J. Rosenthal, “Schubertvariet\ddot aten und deren Singularit\ddot aten,” Diplom Thesis, University of Basel, Switzerland, 1986.




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