Nous donnons une caractérisation des blocs conformes en termes de cohomologie singulière des variétés projectives lisses appropriées, dans le genre pour les algèbres de Lie classiques et .
We give a characterization of conformal blocks in terms of the singular cohomology of suitable smooth projective varieties, in genus for classical Lie algebras and .
Classification : 17B67, 14H60, 32G34, 81T40
Mots clés : blocs conformes, formes logarithmiques, cohomologie singulière
@article{AIF_2014__64_4_1669_0, author = {Belkale, Prakash and Mukhopadhyay, Swarnava}, title = {Conformal blocks and cohomology in genus 0}, journal = {Annales de l'Institut Fourier}, pages = {1669--1719}, publisher = {Association des Annales de l'institut Fourier}, volume = {64}, number = {4}, year = {2014}, doi = {10.5802/aif.2893}, mrnumber = {3329676}, zbl = {06387320}, language = {en}, url = {www.numdam.org/item/AIF_2014__64_4_1669_0/} }
Belkale, Prakash; Mukhopadhyay, Swarnava. Conformal blocks and cohomology in genus 0. Annales de l'Institut Fourier, Tome 64 (2014) no. 4, pp. 1669-1719. doi : 10.5802/aif.2893. http://www.numdam.org/item/AIF_2014__64_4_1669_0/
[1] Integral formulas for the WZNW correlation functions, Nuclear Phys. B, Volume 365 (1991) no. 3, pp. 680-696 | Article | MR 1136712
[2] Conformal blocks, fusion rules and the Verlinde formula, Proceedings of the Hirzebruch 65 Conference on Algebraic Geometry (Ramat Gan, 1993) (Israel Math. Conf. Proc.) Volume 9 (1996), pp. 75-96 | MR 1360497 | Zbl 0848.17024
[3] Unitarity of the KZ/Hitchin connection on conformal blocks in genus 0 for arbitrary Lie algebras, J. Math. Pures Appl. (9), Volume 98 (2012) no. 4, pp. 367-389 | Article | MR 2968161 | Zbl 1277.14035
[4] Factorizable sheaves and quantum groups, Lecture Notes in Mathematics, Volume 1691, Springer-Verlag, Berlin, 1998, pp. x+287 | MR 1641131 | Zbl 0938.17016
[5] Sur les groupes de tresses [d’après V. I. Arnolʼd], Séminaire Bourbaki, 24ème année (1971/1972), Exp. No. 401, Springer, Berlin, 1973, p. 21-44. Lecture Notes in Math., Vol. 317 | Numdam | MR 422674 | Zbl 0277.55003
[6] Théorie de Hodge. II, Inst. Hautes Études Sci. Publ. Math. (1971) no. 40, pp. 5-57 | Article | Numdam | MR 498551 | Zbl 0219.14007
[7] On algebraic equations satisfied by hypergeometric correlators in WZW models. II, Comm. Math. Phys., Volume 170 (1995) no. 1, pp. 219-247 http://projecteuclid.org/euclid.cmp/1104272957 | Article | MR 1331699 | Zbl 0842.17043
[8] Unitarity of -conformal blocks in genus zero, J. Geom. Phys., Volume 59 (2009) no. 5, pp. 654-662 | Article | MR 2518993 | Zbl 1165.32304
[9] The KZ system via polydifferentials, Arrangements of hyperplanes—Sapporo 2009 (Adv. Stud. Pure Math.) Volume 62, Math. Soc. Japan, Tokyo, 2012, pp. 189-231 | MR 2933798 | Zbl 1260.32004
[10] The “Harder-Narasimhan trace” and unitarity of the KZ/Hitchin connection: genus 0, Ann. of Math. (2), Volume 169 (2009) no. 1, pp. 1-39 | Article | MR 2480600 | Zbl 1167.32011
[11] Local systems over complements of hyperplanes and the Kac-Kazhdan conditions for singular vectors, J. Pure Appl. Algebra, Volume 100 (1995) no. 1-3, pp. 93-102 | Article | MR 1344845 | Zbl 0849.32025
[12] Arrangements of hyperplanes and Lie algebra homology, Invent. Math., Volume 106 (1991) no. 1, pp. 139-194 | Article | MR 1123378 | Zbl 0754.17024
[13] Complex semisimple Lie algebras, Springer Monographs in Mathematics, Springer-Verlag, Berlin, 2001, pp. x+74 (Translated from the French by G. A. Jones, Reprint of the 1987 edition) | Article | MR 1808366 | Zbl 1058.17005
[14] La formule de Verlinde, Astérisque (1996) no. 237, pp. Exp. No. 794, 3, 87-114 (Séminaire Bourbaki, Vol. 1994/95) | Numdam | MR 1423621 | Zbl 0878.17024
[15] Vertex operators in conformal field theory on and monodromy representations of braid group, Conformal field theory and solvable lattice models (Kyoto, 1986) (Adv. Stud. Pure Math.) Volume 16, Academic Press, Boston, MA, 1988, pp. 297-372 | MR 972998 | Zbl 0661.17021
[16] Conformal field theory on universal family of stable curves with gauge symmetries, Integrable systems in quantum field theory and statistical mechanics (Adv. Stud. Pure Math.) Volume 19, Academic Press, Boston, MA, 1989, pp. 459-566 | MR 1048605 | Zbl 0696.17010
[17] Conformal field theory with gauge symmetry, Fields Institute Monographs, Volume 24, American Mathematical Society, Providence, RI; Fields Institute for Research in Mathematical Sciences, Toronto, ON, 2008, pp. viii+168 | MR 2433154 | Zbl 1188.81004
[18] Multidimensional hypergeometric functions and representation theory of Lie algebras and quantum groups, Advanced Series in Mathematical Physics, Volume 21, World Scientific Publishing Co., Inc., River Edge, NJ, 1995, pp. x+371 | Article | MR 1384760 | Zbl 0951.33001