Vertex algebras and algebraic curves

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1. [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. Zbl0647.17010MR946992
2. [BL] A. Beauville and Y. Laszlo - Conformal blocks and generalized theta functions, Comm. Math. Phys.164 (1994) 385-419. Zbl0815.14015MR1289330
3. [BB] A. Beilinson and J. Bernstein - A Proof of Jantzen Conjectures, Advances in Soviet Mathematics16, Part 1, pp. 1-50, AMS1993. Zbl0790.22007MR1237825
4. [BD1] A. Beilinson and V. Drinfeld - Affine Kac-Moody algebras and polydifferentials, Int. Math. Res. Notices1 (1994) 1-11. Zbl0830.17013MR1255247
5. [BD2] A. Beilinson and V. Drinfeld - Quantization of Hitchin's Integrable System and Hecke eigensheaves. Preprint. 
6. [BD3] A. Beilinson and V. Drinfeld - Chiral Algebras. Preprint. MR2058353
7. [BFM] A. Beilinson, B. Feigin and B. Mazur - Introduction to Algebraic Field Theory on Curves. Preprint. 
8. [BG] A. Beilinson and V. Ginzburg - Infcnitesimal structure of moduli spaces of G-bundles, Duke Math. J. IMRN4 (1992) 63-74. Zbl0763.32011MR1159447
9. [BS] A. Beilinson and V. Schechtman - Determinant bundles and Virasoro algebras, Comm. Math. Phys.118 (1988) 651-701. Zbl0665.17010MR962493
10. [BPZ] A. Belavin, A. Polyakov and A. Zamolodchikov - Infinite conformal symmetries in two-dimensional quantum field theory, Nucl. Phys. B241 (1984) 333-380. Zbl0661.17013MR757857
11. [BF] D. Ben-Zvi and E. Frenkel - Vertex algebras and algebraic curves, book in preparation. Zbl0981.17022
12. [B1] R. Borcherds - Vertex algebras, Kac-Moody algebras and the monster. Proc. Nat. Acad. Sci. USA83 (1986) 3068-3071. Zbl0613.17012MR843307
13. [B2] R. Borcherds - Monstrous moonshine and monstrous Lie superalgebras, Invent. Math.109 (1992) 405-444. Zbl0799.17014MR1172696
14. [B3] R. Borcherds - Quantum vertex algebras, Preprint math.QA/9903038. MR1865087
15. [Bo1] L. Borisov - Introduction to the vertex algebra approach to mirror symmetry, Preprint math. AG/9912195. 
16. [BoL] L. Borisov and A. Libgober - Elliptic genera of toric varieties and applications to mirror symmetry, Invent. Math.140 (2000) 453-485. Zbl0958.14033MR1757003
17. [dBT] J. de Boer and T. Tjin - The relation between quantum W-algebras and Lie algebras, Comm. Math. Phys.160 (1994) 317-332. Zbl0796.17027MR1262200
18. [dFMS] P. di Francesco, P. Mathieu and D. Senechal - Conformal Field Theory. Springer-Verlag1997. Zbl0869.53052MR1424041
19. [D1] C. Dong - Vertex algebras associated with even lattices, J. Algebra161 (1993) 245-265. Zbl0807.17022MR1245855
20. [D2] C. Dong - Representations of the moonshine module vertex operator algebra, Contemp. Math.175 (1994) 27-36. Zbl0808.17013MR1302010
21. [DLM] C. Dong, H. Li and G. Mason - Twisted representations of vertex operator algebras, Math. Ann.310 (1998) 571-600. Zbl0890.17029MR1615132
22. [DS] V. Drinfeld and V. Sokolov - Lie algebras and KdV type equations, J. Sov. Math.30 (1985) 1975-2036. Zbl0578.58040
23. [EK] P. Etingof and D. Kazhdan - Quantization of Lie bialgebras. V, Preprint math.QA/9808121. Zbl0948.17008
24. [Fa] G. Faltings - A proof of the Verlinde formula, J. Alg. Geom.3 (1994) 347-374. Zbl0809.14009MR1257326
25. [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. MR932661
26. [Fe1] B. Feigin - The semi-infinite cohomology of Kac-Moody and Virasoro Lie algebras, Russ. Math. Surv.39, No. 2 (1984) 155-156. Zbl0574.17008MR740035
27. [FF1] B. Feigin and E. Frenkel - A family of representations of affine Lie algebras, Russ. Math. Surv.43, No. 5 (1988) 221-222. Zbl0668.17015MR971497
28. [FF2] B. Feigin and E. Frenkel - Affine Kac-Moody algebras and semi-infinite flag manifolds, Comm. Math. Phys.128 (1990) 161-189. Zbl0722.17019MR1042449
29. [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. Zbl0925.17022MR1187549
30. [FF4] B. Feigin and E. Frenkel - Integrals of Motion and Quantum Groups, in Lect. Notes in Math.1620, pp. 349-418, Springer-Verlag1996. Zbl0885.58034MR1397275
31. [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. Zbl0857.17021MR1318339
32. [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. Zbl0768.17008MR1174415
33. [FKRW] E. Frenkel, V. Kac, A. Radul and W. Wang - W1+∞ and WN with central charge N, Comm. Math. Phys.170 (1995) 337-357. Zbl0838.17028
34. [FR] E. Frenkel and N. Reshetikhin - Towards deformed chiral algebras, Preprint q-alg/9706023. 
35. [FK] I. Frenkel and V. Kac - Basic representations of affine Lie algebras and dual resonance models, Invent. Math.62 (1980) 23-66. Zbl0493.17010MR595581
36. [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. Zbl0607.17007MR865483
37. [FLM] I. Frenkel, J. Lepowsky and A. Meurman - Vertex Operator Algebras and the Monster. Academic Press1988. Zbl0674.17001MR996026
38. [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. Zbl0789.17022MR1142494
39. [FZ] I. Frenkel and Y. Zhu - Vertex operator algebras associated to representations of affine and Virasoro algebras, Duke Math. J.60 (1992) 123-168. Zbl0848.17032MR1159433
40. [FrS] D. Friedan and S. Shenker - The analytic geometry of two-dirnensional conformal field theory, Nucl. Phys. B281 (1987) 509-545. MR869564
41. [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, AMS1999. Zbl1170.81429MR1701613
42. [Ga] K. Gawędzki - Conformal field theory, Sém. Bourbaki, Exp. 704, Astérisque177-178 (1989) 95-126. Zbl0699.53085MR1040570
43. [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. Zbl0267.18023MR333080
44. [Gi] V. Ginzburg - Resolution of diagonals and moduli spaces, in The moduli space of curves, Progress in Math.129, pp. 231-266, Birkhäuser1995. Zbl0841.14006MR1363059
45. [Go] P. Goddard - Meromorphic conformal field theory, in Infinite-dimensional Lie algebras and groups, V. Kac (ed.), pp. 556-587, World Scientific1989. Zbl0742.17027MR1026966
46. [GKO] P. Goddard, A. Kent and D. Olive - Unitary representations of the Virasoro and super-Virasoro algebras, Comm. Math. Phys.103 (1986) 105- 119. Zbl0588.17014MR826859
47. [GMS] V. Gorbounov, F. Malikov and V. Schechtman - Gerbes of chiral differential operators. I, math.AG/9906116; II, math.AG/0003170. 
48. [Gu] R. Gunning - Lectures on Riemann Surfaces. Princeton University Press1966. Zbl0175.36801MR207977
49. [Hu] Y.-Z. Huang - Two-dimensional conformal geometry and vertex operator algebras. Progress in Math.148. Birkhäuser1997. Zbl0884.17021MR1448404
50. [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, Birkhäuser1996. Zbl0871.17023MR1390314
51. [K1] V. Kac - Infinite-dimensional Lie algebras, Third Edition. Cambridge University Press1990. MR1104219
52. [K2] V. Kac - Vertex Algebras for Beginners, Second Edition. AMS1998. Zbl0924.17023MR1651389
53. [K3] V. Kac - Formal distribution algebras and conformal algebras, in Proc. XXIIth ICMP, Brisbane, 1994, pp. 80-96, International Press1999. MR1697266
54. [KL] D. Kazhdan and G. Lusztig - Tensor structures arising from affine Lie algebras IV, J. of AMS7 (1993) 383-453. Zbl0802.17008MR1239507
55. [Ko] M. Kontsevich - The Virasoro algebra and Teichmüller spaces, Funct. Anal. Appl.21 (1987), no. 2, 156-157. Zbl0647.58012MR902301
56. [KNR] S. Kumar, M.S. Narasimhan and A. Ramanathan - Infinite Grassmannians and moduli spaces of G-bundles, Math. Ann.300 (1993) 395-423. Zbl0803.14012MR1289830
57. [LW] J. Lepowsky and R.L. Wilson - Construction of the affine Lie algebra A(1)1, Comm. Math. Phys.62 (1978) 43-53. Zbl0388.17006MR573075
58. [Li] H. Li - Local systems of vertex operators, vertex superalgebras and modules, J. Pure Appl. Alg.109 (1996) 143-195. Zbl0854.17035MR1387738
59. [LZ] B. Lian and G. ZUCKERMAN - New perspectives on the BRST-algebraic structure of string theory, Comm. Math. Phys.154 (1993) 613-646. Zbl0780.17029MR1224094
60. [MSV] A. Malikov, V. Schechtman and A. Vaintrob - Chiral deRham complex, Comm. Math. Phys.204 (1999) 439-473. Zbl0952.14013MR1704283
61. [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-Verlag1991. Zbl0760.17014MR1260946
62. [Se] G. Segal - The Definition of Conformal Field Theory, unpublished manuscript. 
63. [So] C. Sorger - La formule de Verlinde, Sém. Bourbaki, Exp. 793, Astérisque237 (1996) 87-114. Zbl0878.17024MR1423621
64. [TK] A. Tsuchiya and Y. Kanie - Vertex operators in conformal field theory on P1 and monodromy representations of the braid group, in Adv. Stud. Pure Math16, pp. 297-372, Academic Press1988. Zbl0661.17021MR972998
65. [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 Press1989. Zbl0696.17010MR1048605
66. [Wa] M. Wakimoto - Fock representations of affine Lie algebra A(1)1, Comm. Math. Phys.104 (1986) 605-609. Zbl0587.17009MR841673
67. [Wa] W. Wang - Rationality of Virasoro vertex operator algebras, Duke Math. J. IMRN7 (1993) 197-211. Zbl0791.17029MR1230296
68. [Wi] E. Witten - Quantum field theory, Grassmannians and algebraic curves, Comm. Math. Phys113 (1988) 529-600. Zbl0636.22012MR923632
69. [Z1] Y. Zhu - Modular invariance of characters of vertex operator algebras, J. AMS9 (1996) 237-302. Zbl0854.17034MR1317233
70. [Z2] Y. Zhu - Global vertex operators on Riemann surfaces, Comm. Math. Phys.165 (1994) 485-531. Zbl0819.17019MR1301621

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