Eigenvalue problem and a new product in cohomology of flag varieties

Inventiones Mathematicae

Volumn 166, Issue 1, 2006, Pages 185-228

  Belkale, Prakash ^a   Kumar, Shrawan ^a  

^a University of North Carolina at Chapel Hill   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 33748085407     PISSN: 00209910     EISSN: None     Source Type: Journal    
DOI: 10.1007/s00222-006-0516-x     Document Type: Article

References (34)

1. [AW] Agnihotri, S., Woodward, C.: Eigenvalues of products of unitary matrices and quantum Schubert calculus. Math. Res. Lett. 5, 817-836 (1998)
2. 1-S for S a finite set. Compos. Math. 129, 67-86 (2001)
3. [Bel2] Belkale, P.: Geometric proofs of Horn and saturation conjectures. J. Alg. Geom. 15, 133-173 (2006)
4. [Bel3] Belkale, P.: Invariant theory of GL(n) and intersection theory of Grassmannians. Int. Math. Res. Not. 69, 3709-3721 (2004)
5. [Bel4] Belkale, P.: The quantum horn conjecture. Preprint, math.AG/0303013
6. s}). To appear in the proceedings of the International Colloquium on Algebraic Groups and Homogeneous Spaces (2004), Tata Institute of Fundamental Research, Mumbai
7. [BeSj] Berenstein, A., Sjamaar, R.: Coadjoint orbits, moment polytopes, and the Hilbert-Mumford criterion. J. Am. Math. Soc. 13, 433-466 (2000)
8. [BGG] Bernstein, I.N., Gelfand, I.M., Gelfand, S.I.: Schubert cells and cohomology of the spaces G/P. Russ. Math. Surv. 28, 1-26 (1973)
9. [Bo] Bourbaki, N.: Groupes et Algèbres de Lie, Chap. 4-6. Paris: Masson 1981
10. [Fu1] Fulton, W.: Intersection Theory, 2nd edn. Springer 1998
11. [Fu2] Fulton, W.: Eigenvalues, invariant factors, highest weights, and Schubert calculus. Bull. Am. Math. Soc., New. Ser. 37, 209-249 (2000)
12. [He] Helgason, S.: Differential Geometry, Lie Groups, and Symmetric Spaces. Academic Press 1978
13. [H] Hesselink, W.: Uniform instability in reductive group. J. Reine Angew. Math. 303-304, 74-96 (1978)
14. [J] Jantzen, J.C.: Representations of Algebraic Groups, 2nd edn. Am. Math. Soc. 2003
15. [KaLM] Kapovich, M., Leeb, B., Millson, J.J.: Convex functions on symmetric spaces, side lengths of polygons and the stability inequalities for weighted configurations at infinity. Preprint 2005
16. [Ke] Kempf, G.: Instability in invariant theory. Ann. Math. 108, 299-316 (1978)
17. [K] Kirwan, F.: Cohomology of quotients in symplectic and algebraic geometry. Princeton University Press 1984
18. [Kle] Kleiman, S.L., The transversality of a general translate. Compos. Math. 28, 287-297 (1974)
19. [Kl] Klyachko, A.: Stable bundles, representation theory and Hermitian operators. Sel. Math. 4, 419-445 (1998)
20. n,(ℂ) tensor products I: Proof of the saturation conjecture. J. Am. Math. Soc. 12, 1055-1090 (1999)
21. n(ℂ) tensor products II: Puzzles determine facets of the Littlewood-Richardson cone. J. Am. Math. Soc. 17, 19-48 (2004)
22. [Ko1] Kostant, B.: Lie algebra cohomology and the generalized Borel-Weil theorem. Ann. Math. 74, 329-387 (1961)
23. [Ko2] Kostant. B.: Lie algebra cohomology and generalized Schubert cells. Ann. Math. 77, 72-144 (1963)
24. [KK] Kostant, B., Kumar, S.: The nil Hecke ring and cohomology of G/P for a Kac-Moody group G. Adv. Math. 62, 187-237 (1986)
25. [Ku1] Kumar, S.: Geometry of Schubert cells and cohomology of Kac-Moody Lie algebras. J. Differ. Geom. 20, 389-431 (1984)
26. [Ku2] Kumar, S.: Kac-Moody Groups, their Flag Varieties and Representation Theory. Progress in Mathematics, vol. 204. Birkhäuser 2002
27. [KLM] Kumar, S., Leeb, B., Millson, J.: The generalized triangle inequalities for rank 3 symmetric spaces of noncompact type. Contemp. Math. 332, 171-195 (2003)
28. [MFK] Mumford, D., Fogarty, J., Kirwan, F.: Geometric Invariant Theory, 3rd edn. Ergebnisse der Mathematik und ihrer Grenzgebiete, vol. 34. Springer 1994
29. [P] Purbhoo, K.: Vanishing and non-vanishing criteria in Schubert calculus. Preprint, math. CO/0304070. To appear in Int. Math. Res. Not.
30. [RR] Ramanan, S., Ramanathan, A.: Some remarks on the instability flag. Tôhoku Math. J. 36, 269-291 (1984)
31. [S] Shafarevich, I.R.: Basic Algebraic Geometry I, 2nd edn. Springer 1994
32. [Se] Serre, J.-P.: Complex Semisimple Lie Algebras. Springer 1987
33. [Sj] Sjamaar, R.: Convexity properties of the moment mapping re-examined. Adv. Math. 138, 46-91 (1998)
34. [TW] Teleman, C., Woodward, C.: Parabolic bundles, products of conjugacy classes and Gromov-Witten invariants. Ann. Inst. Fourier 53, 713-748 (2003)