Restriction de représentations et projections d'orbites coadjointes [d'après Belkale, Kumar et Ressayre]
Séminaire Bourbaki volume 2011/2012 exposés 1043-1058, Astérisque, no. 352 (2013), Talk no. 1043, 33 p.
@incollection{AST_2013__352__1_0,
     author = {Brion, Michel},
     title = {Restriction de repr\'esentations et projections d'orbites coadjointes [d'apr\`es {Belkale,} {Kumar} et {Ressayre]}},
     booktitle = {S\'eminaire Bourbaki volume 2011/2012 expos\'es 1043-1058},
     series = {Ast\'erisque},
     note = {talk:1043},
     pages = {1--33},
     publisher = {Soci\'et\'e math\'ematique de France},
     number = {352},
     year = {2013},
     zbl = {1295.22029},
     language = {fr},
     url = {http://www.numdam.org/item/AST_2013__352__1_0/}
}
TY  - CHAP
AU  - Brion, Michel
TI  - Restriction de représentations et projections d'orbites coadjointes [d'après Belkale, Kumar et Ressayre]
BT  - Séminaire Bourbaki volume 2011/2012 exposés 1043-1058
AU  - Collectif
T3  - Astérisque
N1  - talk:1043
PY  - 2013
SP  - 1
EP  - 33
IS  - 352
PB  - Société mathématique de France
UR  - http://www.numdam.org/item/AST_2013__352__1_0/
LA  - fr
ID  - AST_2013__352__1_0
ER  - 
%0 Book Section
%A Brion, Michel
%T Restriction de représentations et projections d'orbites coadjointes [d'après Belkale, Kumar et Ressayre]
%B Séminaire Bourbaki volume 2011/2012 exposés 1043-1058
%A Collectif
%S Astérisque
%Z talk:1043
%D 2013
%P 1-33
%N 352
%I Société mathématique de France
%U http://www.numdam.org/item/AST_2013__352__1_0/
%G fr
%F AST_2013__352__1_0
Brion, Michel. Restriction de représentations et projections d'orbites coadjointes [d'après Belkale, Kumar et Ressayre], in Séminaire Bourbaki volume 2011/2012 exposés 1043-1058, Astérisque, no. 352 (2013), Talk no. 1043, 33 p. http://www.numdam.org/item/AST_2013__352__1_0/

[1] N. Bardy-Panse, C. Charignon, S. Gaussent & G. Rousseau - Applications des immeubles en théorie des représentations, prépublication arXiv: 1007.3803.

[2] P. Belkale - Geometric proofs of Horn and saturation conjectures, J. Algebraic Geom. 15 (2006), n° 1, p. 133-173. | DOI | Zbl

[3] P. Belkale , Geometric proof of a conjecture of Fulton, Adv. Math. 216 (2007), n° 1, p. 346-357. | DOI | Zbl

[4] P. Belkale & S. Kumar - Eigenvalue problem and a new product in cohomology of flag varieties, Invent. Math. 166 (2006), n° 1, p. 185-228. | DOI | Zbl

[5] P. Belkale & S. Kumar , Eigencone, saturation and Horn problems for symplectic and odd orthogonal groups, J. Algebraic Geom. 19 (2010), n° 2, p. 199-242. | DOI | Zbl

[6] P. Belkale, S. Kumar & N. Ressayre - A generalization of Fulton's conjecture for arbitrary groups, Math. Ann. 354 (2012), n° 2, p. 401-425. | DOI | Zbl

[7] A. Berenstein & R. Sjamaar - Coadjoint orbits, moment polytopes, and the Hilbert-Mumford criterion, J. Amer. Math. Soc. 13 (2000), n° 2, p. 433-466. | DOI | Zbl

[8] A. Białynicki-Birula - Some theorems on actions of algebraic groups, Ann. of Math. 98 (1973), p. 480-497. | DOI | Zbl

[9] N. Bourbaki - Éléments de mathématique, Hermann, 1975, Fasc. XXXVIII : Groupes et algèbres de Lie. Chapitre VII : Sous-algèbres de Cartan, éléments réguliers. Chapitre VIII : Algèbres de Lie semi-simples déployées, Actualités Scientifiques et Industrielles, No. 1364. | Zbl

[10] H. Derksen & J. Weyman - Semi-invariants of quivers and saturation for Littlewood-Richardson coefficients, J. Amer. Math. Soc. 13 (2000), n° 3, p. 467-479. | DOI | Zbl

[11] H. Derksen & J. Weyman, The combinatorics of quiver representations, Ann. Inst. Fourier (Grenoble) 61 (2011), n° 3, p. 1061-1131. | DOI | EuDML | Numdam | Zbl

[12] I. V. Dolgachev & Y. Hu - Variation of geometric invariant theory quotients, Publ. Math. I.H.É.S. (1998), n° 87, p. 5-56. | DOI | EuDML | Zbl

[13] V. Guillemin & S. Sternberg - Geometric quantization and multiplicities of group representations, Invent. Math. 67 (1982), n° 3, p. 515-538. | DOI | EuDML | Zbl

[14] G. J. Heckman - Projections of orbits and asymptotic behavior of multiplicities for compact connected Lie groups, Invent. Math. 67 (1982), n° 2, p. 333-356. | DOI | EuDML | Zbl

[15] A. Horn - Eigenvalues of sums of Hermitian matrices, Pacific J. Math. 12 (1962), p. 225-241. | DOI | MR | Zbl

[16] M. Kapovich, S. Kumar & J. J. Millson - The eigencone and saturation for Spin(8), Pure Appl. Math. Q. 5 (2009), n° 2, Special Issue : In honor of Friedrich Hirzebruch. Part 1, p. 755-780. | DOI | MR | Zbl

[17] M. Kapovich, B. Leeb & J. J. Millson - The generalized triangle inequalities in symmetric spaces and buildings with applications to algebra, Mem. Amer. Math. Soc. 192 (2008), n° 896. | MR | Zbl

[18] M. Kapovich & J. J. Millson - A path model for geodesics in Euclidean buildings and its applications to representation theory, Groups Geom. Dyn. 2 (2008), n° 3, p. 405-480. | DOI | MR | Zbl

[19] F. Kirwan - Convexity properties of the moment mapping. III, Invent. Math. 77 (1984), n° 3, p. 547-552. | DOI | EuDML | MR | Zbl

[20] F. C. Kirwan - Cohomology of quotients in symplectic and algebraic geometry, Mathematical Notes, vol. 31, Princeton Univ. Press, 1984. | MR | Zbl

[21] A. A. Klyachko - Stable bundles, representation theory and Hermitian operators, Selecta Math. (N.S.) 4 (1998), n° 3, p. 419-445. | DOI | MR | Zbl

[22] A. Knutson & K. Purbhoo - Product and puzzle formulae for GL n Belkale-Kumar coefficients, Electron. J. Combin. 18 (2011), n° 1, Paper 76, 20 p. | EuDML | MR | Zbl

[23] A. Knutson & T. Tao - The honeycomb model of GL n (𝐂) tensor products. I. Proof of the saturation conjecture, J. Amer. Math. Soc. 12 (1999), n° 4, p. 1055-1090. | DOI | MR | Zbl

[24] A. Knutson, T. Tao & C. Woodward - The honeycomb model of GL n () tensor products. II. Puzzles determine facets of the Littlewood-Richardson cone, J. Amer. Math. Soc. 17 (2004), n° 1, p. 19-48. | DOI | MR | Zbl

[25] B. Kostant - On convexity, the Weyl group and the Iwasawa decomposition, Ann. Sci. École Norm. Sup. 6 (1973), p. 413-455. | DOI | EuDML | Numdam | MR | Zbl

[26] P. Littelmann - Paths and root operators in representation theory, Ann. of Math. 142 (1995), n° 3, p. 499-525. | DOI | MR | Zbl

[27] I. G. Macdonald - Symmetric functions and Hall polynomials, second éd., Oxford Mathematical Monographs, The Clarendon Press Oxford Univ. Press, 1995. | MR

[28] P.-L. Montagard & N. Ressayre - Sur des faces du cône de Littlewood-Richardson généralisé, Bull. Soc. Math. France 135 (2007), n° 3, p. 343-365. | EuDML | Numdam | MR | Zbl

[29] D. Mumford, J. Fogarty & F. C. Kirwan - Geometric invariant theory, 3e éd., Ergebn. Math. Grenzg., vol. 34, Springer, 1994. | MR | Zbl

[30] L. Ness - A stratification of the null cone via the moment map, Amer. J. Math. 106 (1984), n° 6, p. 1281-1329. | DOI | MR | Zbl

[31] N. Ressayre - The GIT-equivalence for G-line bundles, Geom. Dedicata 81 (2000), nos 1-3, p. 295-324. | DOI | MR | Zbl

[32] N. Ressayre, Geometric invariant theory and the generalized eigenvalue problem, Invent. Math. 180 (2010), n° 2, p. 389-441. | DOI | MR | Zbl

[33] N. Ressayre, Geometric invariant theory and generalized eigenvalue problem II, Ann. Inst. Fourier (Grenoble) 61 (2011), n° 4, p. 1467-1491. | DOI | EuDML | Numdam | MR | Zbl

[34] N. Ressayre, A short geometric proof of a conjecture of Fulton, Enseign. Math. 57 (2011), nos 1-2, p. 103-115. | DOI | MR | Zbl

[35] N. Ressayre, Reductions for branching coefficients, prépublication arXiv:1102.0196.

[36] N. Ressayre & E. Richmond - Branching Schubert calculus and the Belkale-Kumar product on cohomology, Proc. Amer. Math. Soc. 139 (2011), n° 3, p. 835-848. | DOI | MR | Zbl

[37] E. Richmond - A partial Horn recursion in the cohomology of flag varieties, J. Algebraic Combin. 30 (2009), n° 1, p. 1-17. | DOI | MR | Zbl

[38] M. Roth - Reduction rules for Littlewood-Richardson coefficients, Int. Math. Res. Not. 2011 (2011), n° 18, p. 4105-4134. | MR | Zbl

[39] S. V. Sam - Symmetric quivers, invariant theory, and saturation theorems for the classical groups, Adv. Math. 229 (2012), n° 2, p. 1104-1135. | DOI | MR | Zbl