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Modular invariance of characters of vertex operator algebras
Author(s):
Yongchang
Zhu
Journal:
J. Amer. Math. Soc.
9
(1996),
237-302.
MSC (1991):
Primary 17B65
MathSciNet review:
1317233
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Additional information
References:
- [Apos]
- T.M.Apostol, Modular functions and Dirichlet series in number theory, Springer-Verlag, 1976, MR 54:10149.
- [Bo]
- R.E. Borcherds, Vertex operator algebras, Kac-Moody algebras and the Monster, Proc. Natl. Acad. Sci. USA. 83 (1986), 3026, MR 87m:17033.
- [BPZ]
- A. Belavin, A.M. Polyakov, A.A. Zamolodchikov, Infinite conformal symmetry in two dimensional quantum field theory, Nucl. Phys. B241 (1984), 33, MR 86m:81097.
- [BS]
- P.Bouwknegt, K.Schoutens,
-symmetry in conformal field theory, Phys. Rep. 223 (1993), MR 94e:81096. - [Ca]
- J.L. Cardy, Operator content of two-dimensional conformal invariant theories, Nucl. Phys. B270 (1986), 186, MR 87k:17017.
- [Do1]
- C.Dong, Representation of the moonshine module vertex operator algebra, preprint, 1992.
- [Do2]
- C.Dong, Vertex algebras associated to even lattice, J. of alg. 161 (1993), MR 94j:17023.
- [DMZ]
- C.Dong, G.Mason, Y.Zhu, Discrete Series of the Virasoro algebra and the moonshine module, Preprint (1991).
- [FFr]
- B.Feigin, E.Frenkel, Affine Kac-Moody algebras at the critical level and Gelfand-Dikii algebras, Int. J. Mod. Phys. A suppl. 1A (1992), MR 93j:17049.
- [Fr]
- I.Frenkel, Orbital theory for affine Lie algebras,, Yale dissertation (1980), or Invent. Math. 77 (1984), MR 86d:17014.
- [F]
- E.Frenkel,
-algebras and Langlands-Drinfeld correspondence, Plenum Press, New York, 1987. - [FF]
- B.L. Feigin, D.B. Fuchs, Verma modules over the Virasoro algebra, Lect. Notes Math., vol 1060, 1984, MR 86g:17004.
- [FKRW]
- E.Frenkel, V.Kac, A.Radul, W.Wang,
and with central charge ., Pre- print (1994). - [FHL]
- I.B. Frenkel, Y. Huang, J.Lepowsky, On axiomatic approaches to vertex operator algebras and modules, preprint, 1989; Memoirs American Math. Soc. 104 (1993), MR 94a:17007.
- [FLM1]
- I.B.Frenkel, J.Lepowsky, A.Meurman, A natural representation of the Fischer-Griess Monster with the modular function J as a character, Proc. Nat. Acad. Sci. USA 81 (1984), 3256-3260, MR 85e:20018.
- [FLM2]
- I.B.Frenkel, J.Lepowsky, A.Meurman, Vertex Operator Algebras and the Monster, Academic Press, New York, 1988, MR 90h:17026.
- [FZ]
- I.B.Frenkel, Y.Zhu, Vertex operator algebras associated to representation of affine and Virasoro algebras, Duke Mathematical Journal 66 (1992), 123, MR 93g:17045.
- [H]
- Y.Z.Huang, Geometric interpretation of vertex operator algebras, Proc. Natl. Acad. Sci. USA 88 (1991), 9964, MR 92k:17037.
- [In]
- E.L. Ince, Ordinary Differential Equations, Dover Publications, Inc, New York, 1956, MR 6:65f.
- [IZ]
- Itsykson, Zuber, Two-dimensional conformal invariant theories on a torus, Nucl.Phys. B275 (1986), MR 88f:8111.
- [K]
- V.G. Kac, Infinite dimensional Lie algebras and Dedekind's
-function, Funct. Anal. Appl. 8 (1974), 68-70, MR 51:10410. - [KP]
- V.G. Kac, D.H.Peterson, Infinite-dimensional Lie algebras, theta functions and modular forms, Advances in Math 53 (1984), 124-264, MR 86a:17007.
- [KW]
- V.G.Kac, M. Wakimoto, Modular and conformal invariance constraints in representation theory, Adv. Math. 70 (1988), MR 89h:17036.
- [La]
- S. Lang, Elliptic Functions, Springer-Verlag, 1987, MR 88c:11028.
- [Li]
- B.Lian, On the classification of simple vert ex operator algebras, preprint (1992).
- [MS]
- G. Moore, N. Seiberg, Classical and quantum conformal field theory, Commun. Math. Phys. 123 (1989), 177-254, MR 90e:81216.
- [R]
- A. Rocha, Vacuum vector representations of the Viraroso algebra, in Vertex Operators in Mathematics and Physics, Spring-Verlag, 1983, MR 87b:17011.
- [TUY]
- A.Tsuchiya, K.Ueno and Y.Yamada, Conformal field theory on universal family of stable curves with gauge symmetries, in Advanced Studies on Pure Math., 1989, MR 92a:81191.
- [T]
- H.Tsukada, String path integral realization of vertex operator algebras, Memoirs of Amer. Math. Soc. 91,no.444 (1991), MR 91m:17044.
- [W]
- N.R.Wallach, Real Reductive Groups I, Academic Press, 1988, MR 89i:22029.
- [Wa]
- W.Wang, Rationality of Virasoro vertex operator algebras, Duke Math. J., IMRN 71, No. 1 (1993), MR 94i:17034.
- [Wi]
- E. Witten, Quantum field theory, Grassmannians, and algebraic curves, Commun. Math. Phys. 113 (1988), 529-600, MR 88m:81127.
- [Z]
- Y.Zhu, Global vertex operators on Riemann surfaces, Commun. Math. Phys. 165 No.3 (1994).
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Additional Information:
Yongchang
Zhu
Affiliation:
Department of Mathematics, Hong Kong University of Science and Technology, Clear Water Bay, Kowloon, Hong Kong
DOI:
10.1090/S0894-0347-96-00182-8
PII:
S 0894-0347(96)00182-8
Received by editor(s):
January 24, 1994
Received by editor(s) in revised form:
January 31, 1995
Copyright of article:
Copyright
1996,
American Mathematical Society
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