Geodesic
Coadjoint orbits, moment polytopes, and the Hilbert-Mumford criterion
Berenstein, Arkady1, 2 ; Sjamaar, Reyer1
1 Department of Mathematics, Cornell University, Ithaca, New York 14853-4201
2 Department of Mathematics, Harvard University, Cambridge, Massachusetts 02138-2901
Journal of the American Mathematical Society, Tome 13 (2000) no. 2, pp. 433-466

Voir la notice de l'article provenant de la source American Mathematical Society

Consider a compact Lie group and a closed subgroup. Generalizing a result of Klyachko, we give a necessary and sufficient criterion for a coadjoint orbit of the subgroup to be contained in the projection of a given coadjoint orbit of the ambient group. The criterion is couched in terms of the “relative” Schubert calculus of the flag varieties of the two groups.
DOI : 10.1090/S0894-0347-00-00327-1

Berenstein, Arkady 1, 2 ; Sjamaar, Reyer 1

1 Department of Mathematics, Cornell University, Ithaca, New York 14853-4201
2 Department of Mathematics, Harvard University, Cambridge, Massachusetts 02138-2901 
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Berenstein, Arkady; Sjamaar, Reyer. Coadjoint orbits, moment polytopes, and the Hilbert-Mumford criterion. Journal of the American Mathematical Society, Tome 13 (2000) no. 2, pp. 433-466. doi: 10.1090/S0894-0347-00-00327-1

[1] Agnihotri, S., Woodward, C. Eigenvalues of products of unitary matrices and quantum Schubert calculus Math. Res. Lett. 1998 817 836

[2] Bernå¡Teä­N, I. N., Gel′Fand, I. M., Gel′Fand, S. I. Schubert cells, and the cohomology of the spaces 𝐺/𝑃 Uspehi Mat. Nauk 1973 3 26

[3] Bourbaki, Nicolas Éléments de mathématique: groupes et algèbres de Lie 1982 138

[4] Demazure, Michel Désingularisation des variétés de Schubert généralisées Ann. Sci. École Norm. Sup. (4) 1974 53 88

[5] Everett, C. J., Jr. Annihilator ideals and representation iteration for abstract rings Duke Math. J. 1939 623 627

[6] Fulton, William Young tableaux 1997

[7] Guillemin, V., Sternberg, S. Convexity properties of the moment mapping Invent. Math. 1982 491 513

[8] Hartshorne, Robin Algebraic geometry 1977

[9] Heckman, G. J. Projections of orbits and asymptotic behavior of multiplicities for compact connected Lie groups Invent. Math. 1982 333 356

[10] Helmke, Uwe, Rosenthal, Joachim Eigenvalue inequalities and Schubert calculus Math. Nachr. 1995 207 225

[11] Guillemin, V., Sternberg, S. Convexity properties of the moment mapping. II Invent. Math. 1984 533 546

[12] Klyachko, Alexander A. Stable bundles, representation theory and Hermitian operators Selecta Math. (N.S.) 1998 419 445

[13] Krã¤Mer, Manfred Über Untergruppen kompakter Liegruppen als Isotropiegruppen bei linearen Aktionen Math. Z. 1976 207 224

[14] Littelmann, Peter A generalization of the Littlewood-Richardson rule J. Algebra 1990 328 368

[15] Montagard, P.-L. Sur les faces du cône associé au pléthysme Comm. Algebra 1998 2321 2336

[16] Mumford, D., Fogarty, J., Kirwan, F. Geometric invariant theory 1994

[17] Pragacz, Piotr Algebro-geometric applications of Schur 𝑆- and 𝑄-polynomials 1991 130 191

[18] Sjamaar, Reyer Convexity properties of the moment mapping re-examined Adv. Math. 1998 46 91

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