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

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

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

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

[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. | MR | Zbl

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

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

[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. | MR | Zbl

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

[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. | MR | Zbl

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

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

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

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

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

[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. | MR | Zbl

[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. | MR | Zbl

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

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

[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. | MR | Zbl

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

[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. | MR | Zbl

[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. | MR | Zbl

[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. | MR | Zbl

[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. | MR | Zbl

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

[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. | MR | Zbl

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

[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. | MR | Zbl

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

[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. | MR | Zbl

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

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

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

[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. | MR | Zbl

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

[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. | MR | Zbl

[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. | MR | Zbl

[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. | MR | Zbl

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

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

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

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

[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. | MR | Zbl

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

[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. | MR | Zbl

[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 | MR | Zbl

[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. | MR | Zbl

[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. | MR | Zbl

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

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

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

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

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