Publications Meetings The Profession Membership Programs Math Samplings Policy & Advocacy In the News About the AMS
|
   
Mobile Device Pairing
 Journal of the American Mathematical Society
Journal of the American Mathematical Society
ISSN 1088-6834(e) ISSN 0894-0347(p)

     

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
Retrieve article in: PDF
This article is available free of charge

References | Similar articles | 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, $W$-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, $W$-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, $W_{1+\infty } $ and $ W( gl_N ) $ with central charge $N$., 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 $\eta $-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).

Similar Articles:

Retrieve articles in Journal of the American Mathematical Society with MSC (1991): 17B65

Retrieve articles in all Journals with MSC (1991): 17B65

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




AMS and Social Media LinkedIn Facebook Podcasts Twitter YouTube RSS Feeds Blogs Wikipedia