Parabolic bundles, products of conjugacy classes, and Gromov-Witten invariants

Constantin Teleman[1]; Christopher Woodward[2]

  • [1] University of Cambridge, DPMMS, CMS, Wilberforce Road, Cambridge CB3 0WB (Grande-Bretagne)
  • [2] Rutgers University, Mathematics, Hill Center, 110 Frelinghuysen Road, Piscataway NJ 08854-8019 (USA)

Annales de l’institut Fourier (2003)

  • Volume: 53, Issue: 3, page 713-748
  • ISSN: 0373-0956

Abstract

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The set of conjugacy classes appearing in a product of conjugacy classes in a compact, 1 -connected Lie group K can be identified with a convex polytope in the Weyl alcove. In this paper we identify linear inequalities defining this polytope. Each inequality corresponds to a non-vanishing Gromov-Witten invariant for a generalized flag variety G / P , where G is the complexification of K and P is a maximal parabolic subgroup. This generalizes the results for S U ( n ) of Agnihotri and the second author and Belkale on the eigenvalues of a product of unitary matrices and quantum cohomology of Grassmannians.

How to cite

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Teleman, Constantin, and Woodward, Christopher. "Parabolic bundles, products of conjugacy classes, and Gromov-Witten invariants." Annales de l’institut Fourier 53.3 (2003): 713-748. <http://eudml.org/doc/116050>.

@article{Teleman2003,
abstract = {The set of conjugacy classes appearing in a product of conjugacy classes in a compact, $1$-connected Lie group $K$ can be identified with a convex polytope in the Weyl alcove. In this paper we identify linear inequalities defining this polytope. Each inequality corresponds to a non-vanishing Gromov-Witten invariant for a generalized flag variety $G/P$, where $G$ is the complexification of $K$ and $P$ is a maximal parabolic subgroup. This generalizes the results for $SU(n)$ of Agnihotri and the second author and Belkale on the eigenvalues of a product of unitary matrices and quantum cohomology of Grassmannians.},
affiliation = {University of Cambridge, DPMMS, CMS, Wilberforce Road, Cambridge CB3 0WB (Grande-Bretagne); Rutgers University, Mathematics, Hill Center, 110 Frelinghuysen Road, Piscataway NJ 08854-8019 (USA)},
author = {Teleman, Constantin, Woodward, Christopher},
journal = {Annales de l’institut Fourier},
keywords = {conjugacy classes; parabolic bundles; quantum cohomology; generalized flag variety; Grassmannians; Schubert calculus},
language = {eng},
number = {3},
pages = {713-748},
publisher = {Association des Annales de l'Institut Fourier},
title = {Parabolic bundles, products of conjugacy classes, and Gromov-Witten invariants},
url = {http://eudml.org/doc/116050},
volume = {53},
year = {2003},
}

TY - JOUR
AU - Teleman, Constantin
AU - Woodward, Christopher
TI - Parabolic bundles, products of conjugacy classes, and Gromov-Witten invariants
JO - Annales de l’institut Fourier
PY - 2003
PB - Association des Annales de l'Institut Fourier
VL - 53
IS - 3
SP - 713
EP - 748
AB - The set of conjugacy classes appearing in a product of conjugacy classes in a compact, $1$-connected Lie group $K$ can be identified with a convex polytope in the Weyl alcove. In this paper we identify linear inequalities defining this polytope. Each inequality corresponds to a non-vanishing Gromov-Witten invariant for a generalized flag variety $G/P$, where $G$ is the complexification of $K$ and $P$ is a maximal parabolic subgroup. This generalizes the results for $SU(n)$ of Agnihotri and the second author and Belkale on the eigenvalues of a product of unitary matrices and quantum cohomology of Grassmannians.
LA - eng
KW - conjugacy classes; parabolic bundles; quantum cohomology; generalized flag variety; Grassmannians; Schubert calculus
UR - http://eudml.org/doc/116050
ER -

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