Vertex algebras and algebraic curves
Séminaire Bourbaki : volume 1999/2000, exposés 865-879, Astérisque, no. 276 (2002), Exposé no. 875, 41 p.

Voir la notice du chapitre de livre provenant de la source Numdam

MR   Zbl

Frenkel, Edward. Vertex algebras and algebraic curves, dans Séminaire Bourbaki : volume 1999/2000, exposés 865-879, Astérisque, no. 276 (2002), Exposé no. 875, 41 p.. http://geodesic.mathdoc.fr/item/SB_1999-2000__42__299_0/
@incollection{SB_1999-2000__42__299_0,
     author = {Frenkel, Edward},
     title = {Vertex algebras and algebraic curves},
     booktitle = {S\'eminaire Bourbaki : volume 1999/2000, expos\'es 865-879},
     series = {Ast\'erisque},
     note = {talk:875},
     pages = {299--339},
     year = {2002},
     publisher = {Soci\'et\'e math\'ematique de France},
     number = {276},
     mrnumber = {1886764},
     zbl = {0997.17015},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/SB_1999-2000__42__299_0/}
}
TY  - CHAP
AU  - Frenkel, Edward
TI  - Vertex algebras and algebraic curves
BT  - Séminaire Bourbaki : volume 1999/2000, exposés 865-879
AU  - Collectif
T3  - Astérisque
N1  - talk:875
PY  - 2002
SP  - 299
EP  - 339
IS  - 276
PB  - Société mathématique de France
UR  - http://geodesic.mathdoc.fr/item/SB_1999-2000__42__299_0/
LA  - en
ID  - SB_1999-2000__42__299_0
ER  - 
%0 Book Section
%A Frenkel, Edward
%T Vertex algebras and algebraic curves
%B Séminaire Bourbaki : volume 1999/2000, exposés 865-879
%A Collectif
%S Astérisque
%Z talk:875
%D 2002
%P 299-339
%N 276
%I Société mathématique de France
%U http://geodesic.mathdoc.fr/item/SB_1999-2000__42__299_0/
%G en
%F SB_1999-2000__42__299_0

[ADKP] E. Arbarello, C. De Concini, V. Kac and C. Procesi - Moduli spaces of curves and representation theory, Comm. Math. Phys. 117 (1988) 1-36. | Zbl | MR

[BL] A. Beauville and Y. Laszlo - Conformal blocks and generalized theta functions, Comm. Math. Phys. 164 (1994) 385-419. | Zbl | MR

[BB] A. Beilinson and J. Bernstein - A Proof of Jantzen Conjectures, Advances in Soviet Mathematics 16, Part 1, pp. 1-50, AMS 1993. | Zbl | MR

[BD1] A. Beilinson and V. Drinfeld - Affine Kac-Moody algebras and polydifferentials, Int. Math. Res. Notices 1 (1994) 1-11. | Zbl | MR

[BD2] A. Beilinson and V. Drinfeld - Quantization of Hitchin's Integrable System and Hecke eigensheaves. Preprint.

[BD3] A. Beilinson and V. Drinfeld - Chiral Algebras. Preprint. | MR

[BFM] A. Beilinson, B. Feigin and B. Mazur - Introduction to Algebraic Field Theory on Curves. Preprint.

[BG] A. Beilinson and V. Ginzburg - Infcnitesimal structure of moduli spaces of G -bundles, Duke Math. J. IMRN 4 (1992) 63-74. | Zbl | MR

[BS] A. Beilinson and V. Schechtman - Determinant bundles and Virasoro algebras, Comm. Math. Phys. 118 (1988) 651-701. | Zbl | MR

[BPZ] A. Belavin, A. Polyakov and A. Zamolodchikov - Infinite conformal symmetries in two-dimensional quantum field theory, Nucl. Phys. B241 (1984) 333-380. | Zbl | MR

[BF] D. Ben-Zvi and E. Frenkel - Vertex algebras and algebraic curves, book in preparation. | Zbl

[B1] R. Borcherds - Vertex algebras, Kac-Moody algebras and the monster. Proc. Nat. Acad. Sci. USA 83 (1986) 3068-3071. | Zbl | MR

[B2] R. Borcherds - Monstrous moonshine and monstrous Lie superalgebras, Invent. Math. 109 (1992) 405-444. | Zbl | MR

[B3] R. Borcherds - Quantum vertex algebras, Preprint math.QA/9903038. | MR

[Bo1] L. Borisov - Introduction to the vertex algebra approach to mirror symmetry, Preprint math. AG/9912195.

[BoL] L. Borisov and A. Libgober - Elliptic genera of toric varieties and applications to mirror symmetry, Invent. Math. 140 (2000) 453-485. | Zbl | MR

[dBT] J. De Boer and T. Tjin - The relation between quantum W -algebras and Lie algebras, Comm. Math. Phys. 160 (1994) 317-332. | Zbl | MR

[dFMS] P. Di Francesco, P. Mathieu and D. Senechal - Conformal Field Theory. Springer-Verlag 1997. | Zbl | MR

[D1] C. Dong - Vertex algebras associated with even lattices, J. Algebra 161 (1993) 245-265. | Zbl | MR

[D2] C. Dong - Representations of the moonshine module vertex operator algebra, Contemp. Math. 175 (1994) 27-36. | Zbl | MR

[DLM] C. Dong, H. Li and G. Mason - Twisted representations of vertex operator algebras, Math. Ann. 310 (1998) 571-600. | Zbl | MR

[DS] V. Drinfeld and V. Sokolov - Lie algebras and K d V type equations, J. Sov. Math. 30 (1985) 1975-2036. | Zbl

[EK] P. Etingof and D. Kazhdan - Quantization of Lie bialgebras. V, Preprint math.QA/9808121. | Zbl

[Fa] G. Faltings - A proof of the Verlinde formula, J. Alg. Geom. 3 (1994) 347-374. | Zbl | MR

[FL] V. Fateev and S. Lukyanov - The models of two-dimensional conformal quantum field theory with Zn symmetry, Int. J. Mod. Phys. A3 (1988), 507- 520. | MR

[Fe1] B. Feigin - The semi-infinite cohomology of Kac-Moody and Virasoro Lie algebras, Russ. Math. Surv. 39, No. 2 (1984) 155-156. | Zbl | MR

[FF1] B. Feigin and E. Frenkel - A family of representations of affine Lie algebras, Russ. Math. Surv. 43, No. 5 (1988) 221-222. | Zbl | MR

[FF2] B. Feigin and E. Frenkel - Affine Kac-Moody algebras and semi-infinite flag manifolds, Comm. Math. Phys. 128 (1990) 161-189. | Zbl | MR

[FF3] B. Feigin and E. Frenkel - Affine Kac-Moody algebras at the critical level and Gelfand-Dikii algebras, Int. Jour. Mod. Phys. A7, Suppl. 1A (1992) 197-215. | Zbl | MR

[FF4] B. Feigin and E. Frenkel - Integrals of Motion and Quantum Groups, in Lect. Notes in Math. 1620, pp. 349-418, Springer-Verlag 1996. | Zbl | MR

[FS] B. Feigin and A. Stoyanovsky - Realization of a modular functor in the space of differentials, and geometric approximation of the moduli space of G-bundles, Funct. Anal. Appl. 28 (1994) 257-275. | Zbl | MR

[FKW] E. Frenkel, V. Kac and M. Wakimoto - Characters and fusion rules for W -algebras via quantized Drinfeld-Sokolov reduction, Comm. Math. Phys. 147 (1992), 295-328. | Zbl | MR

[FKRW] E. Frenkel, V. Kac, A. Radul and W. Wang - W 1 + and W N with central charge N , Comm. Math. Phys. 170 (1995) 337-357. | Zbl

[FR] E. Frenkel and N. Reshetikhin - Towards deformed chiral algebras, Preprint q-alg/9706023.

[FK] I. Frenkel and V. Kac - Basic representations of affine Lie algebras and dual resonance models, Invent. Math. 62 (1980) 23-66. | Zbl | MR

[FGZ] I. Frenkel, H. Garland and G. Zuckerman - Semi-infinite cohomology and string theory, Proc. Nat. Acad. Sci. U.S. A. 83 (1986) 8442-8446. | Zbl | MR

[FLM] I. Frenkel, J. Lepowsky and A. Meurman - Vertex Operator Algebras and the Monster. Academic Press 1988. | Zbl | MR

[FHL] I. Frenkel, Y.-Z. Huang and J. Lepowsky - On axiomatic approaches to vertex operator algebras and modules. Mem. Amer. Math. Soc. 104 (1993), no. 494. | Zbl | MR

[FZ] I. Frenkel and Y. Zhu - Vertex operator algebras associated to representations of affine and Virasoro algebras, Duke Math. J. 60 (1992) 123-168. | Zbl | MR

[FrS] D. Friedan and S. Shenker - The analytic geometry of two-dirnensional conformal field theory, Nucl. Phys. B281 (1987) 509-545. | MR

[G] D. Gaitsgory - Notes on 2D Conformal Field Theory and String Theory, in Quantum fields and strings: a course for mathematicians, Vol. 2, pp. 1017-1089, AMS 1999. | Zbl | MR

[Ga] K. Gawędzki - Conformal field theory, Sém. Bourbaki, Exp. 704, Astérisque 177-178 (1989) 95-126. | Numdam | Zbl | MR

[GKF] I. M. Gelfand, D. A. Kazhdan and D. B. Fuchs - The actions of infinite-dimensional Lie algebras, Funct. Anal. Appl. 6 (1972) 9-13. | Zbl | MR

[Gi] V. Ginzburg - Resolution of diagonals and moduli spaces, in The moduli space of curves, Progress in Math. 129, pp. 231-266, Birkhäuser 1995. | Zbl | MR

[Go] P. Goddard - Meromorphic conformal field theory, in Infinite-dimensional Lie algebras and groups, V. Kac (ed.), pp. 556-587, World Scientific 1989. | Zbl | MR

[GKO] P. Goddard, A. Kent and D. Olive - Unitary representations of the Virasoro and super-Virasoro algebras, Comm. Math. Phys. 103 (1986) 105- 119. | Zbl | MR

[GMS] V. Gorbounov, F. Malikov and V. Schechtman - Gerbes of chiral differential operators. I, math.AG/9906116; II, math.AG/0003170.

[Gu] R. Gunning - Lectures on Riemann Surfaces. Princeton University Press 1966. | Zbl | MR

[Hu] Y.-Z. Huang - Two-dimensional conformal geometry and vertex operator algebras. Progress in Math. 148. Birkhäuser 1997. | Zbl | MR

[HL] Y.-Z. Huang and J. Lepowsky - On the 𝒟 -module and formal variable approaches to vertex algebras, in Topics in geometry, pp. 175-202, Birkhäuser 1996. | Zbl | MR

[K1] V. Kac - Infinite-dimensional Lie algebras, Third Edition. Cambridge University Press 1990. | MR

[K2] V. Kac - Vertex Algebras for Beginners, Second Edition. AMS 1998. | Zbl | MR

[K3] V. Kac - Formal distribution algebras and conformal algebras, in Proc. XXIIth ICMP, Brisbane, 1994, pp. 80-96, International Press 1999. | MR

[KL] D. Kazhdan and G. Lusztig - Tensor structures arising from affine Lie algebras IV, J. of AMS 7 (1993) 383-453. | Zbl | MR

[Ko] M. Kontsevich - The Virasoro algebra and Teichmüller spaces, Funct. Anal. Appl. 21 (1987), no. 2, 156-157. | Zbl | MR

[KNR] S. Kumar, M. S. Narasimhan and A. Ramanathan - Infinite Grassmannians and moduli spaces of G-bundles, Math. Ann. 300 (1993) 395-423. | Zbl | MR

[LW] J. Lepowsky and R. L. Wilson - Construction of the affine Lie algebra A 1 ( 1 ) , Comm. Math. Phys. 62 (1978) 43-53. | Zbl | MR

[Li] H. Li - Local systems of vertex operators, vertex superalgebras and modules, J. Pure Appl. Alg. 109 (1996) 143-195. | Zbl | MR

[LZ] B. Lian and G. Zuckerman - New perspectives on the B R S T -algebraic structure of string theory, Comm. Math. Phys. 154 (1993) 613-646. | Zbl | MR

[MSV] A. Malikov, V. Schechtman and A. Vaintrob - Chiral deRham complex, Comm. Math. Phys. 204 (1999) 439-473. | Zbl | MR

[SV2] V. Schechtman and A. Varchenko - Quantum groups and homology of local systems, in Algebraic Geometry and Analytic Geometry, M. Kashiwara and T. Miwa (eds.), pp. 182-191, Springer-Verlag 1991. | Zbl | MR

[Se] G. Segal - The Definition of Conformal Field Theory, unpublished manuscript.

[So] C. Sorger - La formule de Verlinde, Sém. Bourbaki, Exp. 793, Astérisque 237 (1996) 87-114. | Numdam | Zbl | MR

[TK] A. Tsuchiya and Y. Kanie - Vertex operators in conformal field theory on 1 and monodromy representations of the braid group, in Adv. Stud. Pure Math 16, pp. 297-372, Academic Press 1988. | Zbl | MR

[TUY] A. Tsuchiya, K. Ueno and Y. Yamada - Conformal field theory on universal family of stable curves with gauge symmetries, Adv. Stud. Pure Math. 19, pp. 459-566, Academic Press 1989. | Zbl | MR

[Wa] M. Wakimoto - Fock representations of affine Lie algebra A 1 ( 1 ) , Comm. Math. Phys. 104 (1986) 605-609. | Zbl | MR

[Wa] W. Wang - Rationality of Virasoro vertex operator algebras, Duke Math. J. IMRN 7 (1993) 197-211. | Zbl | MR

[Wi] E. Witten - Quantum field theory, Grassmannians and algebraic curves, Comm. Math. Phys 113 (1988) 529-600. | Zbl | MR

[Z1] Y. Zhu - Modular invariance of characters of vertex operator algebras, J. AMS 9 (1996) 237-302. | Zbl | MR

[Z2] Y. Zhu - Global vertex operators on Riemann surfaces, Comm. Math. Phys. 165 (1994) 485-531. | Zbl | MR