The set of conjugacy classes appearing in a product of conjugacy classes in a compact, -connected Lie group 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 , where is the complexification of and is a maximal parabolic subgroup. This generalizes the results for of Agnihotri and the second author and Belkale on the eigenvalues of a product of unitary matrices and quantum cohomology of Grassmannians.
L’ensemble des classes de conjugaison apparaissant dans un produit de classes de conjugaison d’un groupe de Lie 1-connexe compact peut être identifié avec un polytope convexe dans une chambre pour le groupe affine de Weyl. Nous démontrons que les inégalités linéaires définissant ce polytope correspondent aux invariants de Gromov- Witten pour les variétés de drapeaux généralisées. Ceci généralise les résultats de Agnihotri, du deuxième auteur et de Belkale sur les valeurs propres d’un produit de matrices unitaires et la cohomologie quantique des grassmanniennes.
Keywords: conjugacy classes, parabolic bundles, quantum cohomology
@article{AIF_2003__53_3_713_0, author = {Teleman, Constantin and Woodward, Christopher}, title = {Parabolic bundles, products of conjugacy classes, and {Gromov-Witten} invariants}, journal = {Annales de l'Institut Fourier}, pages = {713--748}, publisher = {Association des Annales de l{\textquoteright}institut Fourier}, volume = {53}, number = {3}, year = {2003}, doi = {10.5802/aif.1957}, zbl = {1041.14025}, mrnumber = {2008438}, language = {en}, url = {https://aif.centre-mersenne.org/articles/10.5802/aif.1957/} }
TY - JOUR TI - Parabolic bundles, products of conjugacy classes, and Gromov-Witten invariants JO - Annales de l'Institut Fourier PY - 2003 DA - 2003/// SP - 713 EP - 748 VL - 53 IS - 3 PB - Association des Annales de l’institut Fourier UR - https://aif.centre-mersenne.org/articles/10.5802/aif.1957/ UR - https://zbmath.org/?q=an%3A1041.14025 UR - https://www.ams.org/mathscinet-getitem?mr=2008438 UR - https://doi.org/10.5802/aif.1957 DO - 10.5802/aif.1957 LA - en ID - AIF_2003__53_3_713_0 ER -
Teleman, Constantin; Woodward, Christopher. Parabolic bundles, products of conjugacy classes, and Gromov-Witten invariants. Annales de l'Institut Fourier, Volume 53 (2003) no. 3, pp. 713-748. doi : 10.5802/aif.1957. https://aif.centre-mersenne.org/articles/10.5802/aif.1957/
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