Pieri-type formulas for maximal isotropic Grassmannians via triple intersections

Frank Sottile

Colloquium Mathematicae (1999)

  • Volume: 82, Issue: 1, page 49-63
  • ISSN: 0010-1354

Abstract

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We give an elementary proof of the Pieri-type formula in the cohomology ring of a Grassmannian of maximal isotropic subspaces of an orthogonal or symplectic vector space. This proof proceeds by explicitly computing a triple intersection of Schubert varieties. The multiplicities (which are powers of 2) in the Pieri-type formula are seen to arise from the intersection of a collection of quadrics with a linear space.

How to cite

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Sottile, Frank. "Pieri-type formulas for maximal isotropic Grassmannians via triple intersections." Colloquium Mathematicae 82.1 (1999): 49-63. <http://eudml.org/doc/210750>.

@article{Sottile1999,
abstract = {We give an elementary proof of the Pieri-type formula in the cohomology ring of a Grassmannian of maximal isotropic subspaces of an orthogonal or symplectic vector space. This proof proceeds by explicitly computing a triple intersection of Schubert varieties. The multiplicities (which are powers of 2) in the Pieri-type formula are seen to arise from the intersection of a collection of quadrics with a linear space.},
author = {Sottile, Frank},
journal = {Colloquium Mathematicae},
keywords = {Schubert varieties; isotropic grassmannians; triple intersections; Pieri formulas; intersection multiplicities},
language = {eng},
number = {1},
pages = {49-63},
title = {Pieri-type formulas for maximal isotropic Grassmannians via triple intersections},
url = {http://eudml.org/doc/210750},
volume = {82},
year = {1999},
}

TY - JOUR
AU - Sottile, Frank
TI - Pieri-type formulas for maximal isotropic Grassmannians via triple intersections
JO - Colloquium Mathematicae
PY - 1999
VL - 82
IS - 1
SP - 49
EP - 63
AB - We give an elementary proof of the Pieri-type formula in the cohomology ring of a Grassmannian of maximal isotropic subspaces of an orthogonal or symplectic vector space. This proof proceeds by explicitly computing a triple intersection of Schubert varieties. The multiplicities (which are powers of 2) in the Pieri-type formula are seen to arise from the intersection of a collection of quadrics with a linear space.
LA - eng
KW - Schubert varieties; isotropic grassmannians; triple intersections; Pieri formulas; intersection multiplicities
UR - http://eudml.org/doc/210750
ER -

References

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  13. [13] P. Pragacz and J. Ratajski, Pieri type formula for isotropic Grassmannians; the operator approach, Manuscripta Math. 79 (1993), 127-151. Zbl0789.14041
  14. [14] P. Pragacz and J. Ratajski, Pieri-type formula for Lagrangian and odd orthogonal Grassmannians, J. Reine Angew. Math. 476 (1996), 143-189. Zbl0847.14029
  15. [15] P. Pragacz and J. Ratajski, A Pieri-type theorem for even orthogonal Grassmannians, Max-Planck Institut preprint, 1996. Zbl0847.14029
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  17. [17] F. Sottile, Pieri's formula for flag manifolds and Schubert polynomials, Ann. Inst. Fourier (Grenoble) 46 (1996), 89-110. Zbl0837.14041

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