La formule de Verlinde

Séminaire Bourbaki : volume 1994/95, exposés 790-804, Astérisque no. 237 (1996), Talk no. 794, p. 87-114

MR 1423621 | Zbl 0878.17024 | 5 citations in Numdam

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     author = {Sorger, Christoph},
     title = {La formule de Verlinde},
     booktitle = {S\'eminaire Bourbaki : volume 1994/95, expos\'es 790-804},
     author = {Collectif},
     series = {Ast\'erisque},
     publisher = {Soci\'et\'e math\'ematique de France},
     number = {237},
     year = {1996},
     note = {talk:794},
     pages = {87-114},
     zbl = {0878.17024},
     mrnumber = {1423621},
     language = {fr},
     url = {http://www.numdam.org/item/SB_1994-1995__37__87_0}
}

Sorger, Christoph. La formule de Verlinde, in Séminaire Bourbaki : volume 1994/95, exposés 790-804, Astérisque, no. 237 (1996), Talk no. 794, pp. 87-114. http://www.numdam.org/item/SB_1994-1995__37__87_0/

References

[1] A. Beauville. Conformal Blocks, Fusion rules and the Verlinde formula, Prépublication alg-geom/9405001 (1994) | MR 1360497 | Zbl 0848.17024

[2] A. Beauville ET Y. Laszlo. Conformal blocks and generalized theta functions, Comm. Math. Physics 164 (1994) 385-419 | Article | MR 1289330 | Zbl 0815.14015

[3] A. Beauville, M. S. Narasimhan ET S. Ramanan. Spectral curves and the generalised theta divisor, J. reine angew. Math. 398 (1989) 169-179 | MR 998478 | Zbl 0666.14015

[4] A. Beilinson ET V. Schechtmann. Determinant bundles and Virasoro algebras, Comm. Math. Phys. 118 (1988) 651-701 | Article | MR 962493 | Zbl 0665.17010

[5] A. Bertram. Generalized SU(2)-theta functions, Inv. Math. 113 (1993) 351-372 | Article | MR 1228129 | Zbl 0816.14013

[6] A. Bertram ET A. Szenes. Hilbert polynomials of moduli spaces of rank 2 vector bundles II, Topology 32 (1993) 599-609 | Article | MR 1231966 | Zbl 0798.14004

[7] G. Daskalopoulos ET R. Wentworth. Local degeneration of the moduli space of vector bundles and factorisation of rank 2 theta functions, Math. Annalen 297 (1992) 417-466 | Article | MR 1245399 | Zbl 0788.32012

[8] G. Daskalopoulos ET R. Wentworth. Factorisation of rank 2 theta functions II: the Verlinde formula, Prépublication (1994) | Zbl 0847.32020

[9] R. Donagi ET L. Tu. Theta functions for SL(n) versus GL(n), Prépublication (1992) | Zbl 0847.14027

[10] S. Donaldson. Gluing techniques in the cohomology of moduli spaces, à paraître au volume en mémoire de Andreas Floer (edité par H. Hofer, C. Taubes, E. Zehnder) (1994) | MR 1224262 | MR 1215963 | Zbl 0870.57039

[11] J. M. Drezet ET M. S. Narasimhan. Groupe de Picard des variétés de modules de fibrés semi-stables sur les courbes algébriques., Invent. math. 97 (1989) 53-94 | Article | MR 999313 | Zbl 0689.14012

[12] G. Faltings. G-bundles and projective connections, J. Alg. Geometry 2 (1993) 507-568 | MR 1211997 | Zbl 0790.14019

[13] G. Faltings. A proof of the Verlinda formula, J. Alg. Geometry 3 (1994) 347- 374 | MR 1257326 | Zbl 0809.14009

[14] N. Hitchin. Flat connections and geometric quantization, Comm. Math. Phys. 131 (1990) 347-380 | Article | MR 1065677 | Zbl 0718.53021

[15] V. Kac. Infinite Dimensional Lie Algebras, Cambridge University Press, Cambridge (1985) | MR 823672 | Zbl 0574.17010

[16] V. Knizhnik ET A. Zamolodchikov. Current algebra and Wess-Zumino model in two dimensions, Nucl. Phys. B 247 (1984) | Article | MR 853258 | Zbl 0661.17020

[17] S. Kumar. Demazure character formula in arbitrary Kac-Moody setting, Inv. math. 89 (1987) 395-423 | Article | MR 894387 | Zbl 0635.14023

[18] S. Kumar, M. S. Narasimhan ET A. Ramanathan. Infinite Grassmanians and Moduli Spaces of G-bundles, Math. Annalen 300 (1993) 395-423 | MR 1289830 | Zbl 0803.14012

[19] O. Mathieu. Formules de caractères pour les algèbres de Kac-Moody générales, Astérisque 159-160 (1988) | Numdam | MR 980506 | Zbl 0683.17010 | Zbl 00041944

[20] M. S. Narasimhan ET T. R. Ramadas. Factorisation of generalized Theta functions I, Inv. Math. 114 (1993) 565-623 | Article | MR 1244913 | Zbl 0815.14014

[21] W. M. Oxbury ET S. M. J. Wilson. Reciprocity laws in the Verlinde formulae for classical groups, Prépublication, Durham University (1994) | Zbl 0902.14031

[22] T. Panteev. Comparison of generalized theta functions, Prépublication (1993) | Zbl 0843.14013

[23] C. Pauly. Espaces de modules de fibrés paraboliques et blocs conformes, Prépublication (1994) | Zbl 0877.14031

[24] T. R. Ramadas. Factorisation of generalized theta functions II, Prépublication, TIFR Bombay (1994) | Zbl 0852.14007

[25] G. Segal ET G. Wilson. Loop groups and equations of KdV type, Pub. math. IHES 61 (1985) 5-65 | Article | Numdam | MR 783348 | Zbl 0592.35112

[26] A. Szenes. Hilbert polynomials of moduli spaces of rank 2 vector bundles I, Topology 32 (1993.1) 587-597 | Article | MR 1231965 | Zbl 0798.14003

[27] A. Szenes. The combinatorics of the Verlinde formulas, Prépublication (1994) | MR 1338418 | Zbl 0823.14019

[28] M. Thaddeus. Stable pairs, linear systems and the Verlinde formula, Inv. Math. 117 (1994) | Article | MR 1273268 | Zbl 0882.14003

[29] Y. Tsuchimoto. On the coordinate-free description of the conformal blocks, J. Math. Kyoto Univ. 33 (1993) 29-49 | Article | MR 1203889 | Zbl 0790.14022

[30] A. Tsuchiya, K. Ueno ET Y. Yamada. Conformal Field Theory on Universal Family of Stable Curves with Gauge Symmetries, Adv. Studies in Pure Math. 19 (1989) 459-566 | Article | MR 1048605 | Zbl 0696.17010

[31] A. Tyurin. On periods of quadratic differentials, Russ. Math. Surv. 33 No. 3 (1978) 159 | MR 526014 | Zbl 0429.30037

[32] E. Verlinde. Fusion rules and modular transformations in 2d-conformal field theory., Nucl. Phys. B 300 (1988) 360-376 | Article | MR 954762 | Zbl 1180.81120

[33] D. Zagier. On the cohomolgy of moduli spaces of rank two vector bundles over curves, (1991) | Zbl 0845.14016

[34] D. Zagier. Values of the zeta function and their applications, à paraître dans les annales du congrès européen des mathématiques (1992)