La dualité étrange [d'après P. Belkale, A. Marian et D. Oprea]
Séminaire Bourbaki Volume 2007/2008 Exposés 982-996, Astérisque, no. 326 (2009), Talk no. 994, 15 p.
@incollection{AST_2009__326__363_0,
     author = {Pauly, Christian},
     title = {La dualit\'e \'etrange [d'apr\`es {P.} {Belkale,} {A.} {Marian} et {D.} {Oprea]}},
     booktitle = {S\'eminaire Bourbaki Volume 2007/2008 Expos\'es 982-996},
     author = {Collectif},
     series = {Ast\'erisque},
     note = {talk:994},
     publisher = {Soci\'et\'e math\'ematique de France},
     number = {326},
     year = {2009},
     zbl = {1190.14030},
     mrnumber = {2605328},
     language = {fr},
     url = {http://archive.numdam.org/item/AST_2009__326__363_0/}
}
TY  - CHAP
AU  - Pauly, Christian
TI  - La dualité étrange [d'après P. Belkale, A. Marian et D. Oprea]
BT  - Séminaire Bourbaki Volume 2007/2008 Exposés 982-996
AU  - Collectif
T3  - Astérisque
N1  - talk:994
PY  - 2009
DA  - 2009///
IS  - 326
PB  - Société mathématique de France
UR  - http://archive.numdam.org/item/AST_2009__326__363_0/
UR  - https://zbmath.org/?q=an%3A1190.14030
UR  - https://www.ams.org/mathscinet-getitem?mr=2605328
LA  - fr
ID  - AST_2009__326__363_0
ER  - 
%0 Book Section
%A Pauly, Christian
%T La dualité étrange [d'après P. Belkale, A. Marian et D. Oprea]
%B Séminaire Bourbaki Volume 2007/2008 Exposés 982-996
%A Collectif
%S Astérisque
%Z talk:994
%D 2009
%N 326
%I Société mathématique de France
%G fr
%F AST_2009__326__363_0
Pauly, Christian. La dualité étrange [d'après P. Belkale, A. Marian et D. Oprea], in Séminaire Bourbaki Volume 2007/2008 Exposés 982-996, Astérisque, no. 326 (2009), Talk no. 994, 15 p. http://archive.numdam.org/item/AST_2009__326__363_0/

[1] T. Abe - Strange duality for parabolic symplectic bundles on a pointed projective line, Int. Math. Res. Not. IMRN (2008), art. ID rnn121. | MR | Zbl

[2] T. Abe -, Degeneration of the strange duality map for symplectic bundles, à paraître dans J. reine angew. Math. | MR | Zbl

[3] A. Beauville - Vector bundles on curves and generalized theta functions : recent results and open problems, in Current topics in complex algebraic geometry (Berkeley, CA, 1992/93), Math. Sci. Res. Inst. Publ., vol. 28, Cambridge Univ. Press, 1995, p. 17-33. | MR | Zbl

[4] A. Beauville -, Orthogonal bundles on curves and theta functions, Ann. Inst Fourier (Grenoble) 56 (2006), p. 1405-1418. | DOI | EuDML | Numdam | MR | Zbl

[5] A. Beauville, M. S. Narasimhan & S. Ramanan - Spectral curves and the generalised theta divisor, J. reine angew. Math. 398 (1989), p. 169-179. | EuDML | MR | Zbl

[6] P. Belkale - The strange duality conjecture for generic curves, J. Amer. Math. Soc. 21 (2008), p. 235-258. | DOI | MR | Zbl

[7] P. Belkale -, Orthogonal bundles, theta characteristics and the symplectic strange duality, prépublication arXiv:0808.0863. | DOI | MR | Zbl

[8] P. Belkale -, Strange duality and the Hitchin/WZW connection, prépublication arXiv:0705.0717. | DOI | MR | Zbl

[9] A. Bertram - Towards a Schubert calculus for maps from a Riemann surface to a Grassmannian, Internat. J. Math. 5 (1994), p. 811-825. | DOI | MR | Zbl

[10] A. Bertram, G. Daskalopoulos & R. Wentworth - Gromov invariants for holomorphic maps from Riemann surfaces to Grassmannians, J. Amer. Math. Soc. 9 (1996), p. 529-571. | DOI | MR | Zbl

[11] A. Boysal & C. Pauly - Strange duality for verlinde spaces of exceptional groups at level 1, prepublication, 2008. | Zbl

[12] R. Donagi & L. W. Tu - Theta functions for S L ( n ) versus G L ( n ) , Math. Res. Lett. 1 (1994), p. 345-357. | DOI | MR | Zbl

[13] J.-M. Drezet & M. S. Narasimhan - Groupe de Picard des variétés de modules de fibrés semi-stables sur les courbes algébriques, Invent Math. 97 (1989), p. 53-94. | DOI | EuDML | MR | Zbl

[14] N. J. Hitchin - Flat connections and geometric quantization, Comm. Math. Phys. 131 (1990), p. 347-380. | DOI | MR | Zbl

[15] S. L. Kleiman - The transversality of a general translate, Compositio Math. 28 (1974), p. 287-297. | EuDML | Numdam | MR | Zbl

[16] J. Le Potier - Lectures on vector bundles, Cambridge Studies in Advanced Mathematics, vol. 54, Cambridge University Press, 1997. | MR | Zbl

[17] A. Marian & D. Oprea - The level-rank duality for non-abelian theta functions, Invent Math. 168 (2007), p. 225-247. | DOI | MR | Zbl

[18] A. Marian & D. Oprea -, Virtual intersections on the Quot scheme and Vafa-Intriligator formulas, Duke Math. J. 136 (2007), p. 81-113. | DOI | MR | Zbl

[19] A. Marian & D. Oprea -, A tour of theta dualities on moduli spaces of sheaves, prepublication arXiv:0710.2908. | DOI | MR | Zbl

[20] D. Mumford - Prym varieties. I, in Contributions to analysis (a collection of papers dedicated to Lipman Bers), Academic Press, 1974, p. 325-350. | MR | Zbl

[21] S. G. Naculich & H. J. Schnitzer - Duality relations between S U ( N ) k and S U ( k ) N WZW models and their braid matrices, Phys. Lett. B 244 (1990), p. 235-240. | DOI | MR

[22] T. Nakanishi & A. Tsuchiya - Level-rank duality of WZW models in conformal field theory, Comm. Math. Phys. 144 (1992), p. 351-372. | DOI | MR | Zbl

[23] R. Oudompheng - Rank-level duality for conformal blocks of G L n and S L n , prepublication arXiv:0805.1738.

[24] W. M. Oxbury & S. M. J. Wilson - Reciprocity laws in the Verlinde formulae for the classical groups, Trans. Amer. Math. Soc. 348 (1996), p. 2689-2710. | DOI | MR | Zbl

[25] C. Pauly - Espaces de modules de fibres paraboliques et blocs conformes, Duke Math. J. 84 (1996), p. 217-235. | MR | Zbl

[26] C. Pauly & S. Ramanan - A duality for spin Verlinde spaces and Prym theta functions, J. London Math. Soc. 63 (2001), p. 513-532. | DOI | MR | Zbl

[27] M. Popa - Generalized theta linear series on moduli spaces of vector bundles on curves, prepublication arXiv:0712.3192. | MR | Zbl

[28] A. N. Schellekens & N. P. Warner - Conformal subalgebras of Kac-Moody algebras, Phys. Rev. D 34 (1986), p. 3092-3096. | DOI | MR

[29] B. Siebert & G. Tian - On quantum cohomology rings of Fano manifolds and a formula of Vafa and Intriligator, Asian J. Math. 1 (1997), p. 679-695. | DOI | MR | Zbl

[30] C. Sorger - La formule de Verlinde, Astérisque 237 (1996), p. 87-114, Séminaire Bourbaki, Vol. 1994/95, exposé n° 794. | EuDML | Numdam | MR | Zbl

[31] C. Sorger -, On moduli of G-bundles of a curve for exceptional G, Ann. Sci. École Norm. Sup. 32 (1999), p. 127-133. | DOI | EuDML | Numdam | MR | Zbl

[32] A. Tsuchiya, K. Ueno & Y. Yamada - Conformal field theory on universal family of stable curves with gauge symmetries, in Integrable systems in quantum field theory and statistical mechanics, Adv. Stud. Pure Math., vol. 19, Academic Press, 1989, p. 459-566. | MR | Zbl

[33] E. Witten - The Verlinde algebra and the cohomology of the Grassmannian, in Geometry, topology, & physics, Conf. Proc. Lecture Notes Geom. Topology, IV, Int. Press, Cambridge, MA, 1995, p. 357-422. | MR | Zbl