Vertex operator algebras associated to representations of affine and Virasoro algebras
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Vertex operator algebras associated to representations of affine and Virasoro algebras

Igor B. Frenkel and Yongchang Zhu

Source: Duke Math. J. Volume 66, Number 1 (1992), 123-168.

First Page PDF: View first page of article (PDF, 126 KB)

Primary Subjects: 17B68
Secondary Subjects: 17B67

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Links and Identifiers

Permanent link to this document: http://projecteuclid.org/euclid.dmj/1077294666
Mathematical Reviews number (MathSciNet): MR1159433
Zentralblatt MATH identifier: 0848.17032
Digital Object Identifier: doi:10.1215/S0012-7094-92-06604-X

References

[BPZ] A. A. Belavin, A. M. Polyakov, and A. B. Zamolodchikov, Infinite conformal symmetry in two-dimensional quantum field theory, Nuclear Phys. B 241 (1984), no. 2, 333–380.
Mathematical Reviews (MathSciNet): MR86m:81097
Zentralblatt MATH: 0661.17013
Digital Object Identifier: doi:10.1016/0550-3213(84)90052-X
[B] R. E. Borcherds, Vertex algebras, Kac-Moody algebras, and the Monster, Proc. Nat. Acad. Sci. U.S.A. 83 (1986), no. 10, 3068–3071.
Mathematical Reviews (MathSciNet): MR87m:17033
Zentralblatt MATH: 0613.17012
Digital Object Identifier: doi:10.1073/pnas.83.10.3068
[DVVV] R. Dijkgraaf, C. Vafa, E. Verlinde, and H. Verlinde, The operator algebra of orbifold models, Comm. Math. Phys. 123 (1989), no. 3, 485–526.
Mathematical Reviews (MathSciNet): MR91c:81132
Zentralblatt MATH: 0674.46051
Digital Object Identifier: doi:10.1007/BF01238812
[DL] C. Y. Dong and J. Lepowsky, A Jacobi identity for relative vertex operators and the equivalence of $Z$-algebras and parafermion algebras, XVIIth International Colloquium on Group Theoretical Methods in Physics (Sainte-Adèle, PQ, 1988) ed. Y. Saint-Aubin, World Sci. Publishing, Teaneck, NJ, 1989, pp. 235–238.
Mathematical Reviews (MathSciNet): MR92i:17032
[D] V. G. Drinfeld, Quasi-Hopf algebras, Algebra i Analiz 1 (1989), no. 6, 114–148.
Mathematical Reviews (MathSciNet): MR91b:17016
Zentralblatt MATH: 0718.16033
[FFR] A. Feingold, I. B. Frenkel, and J. Ries, Spinor construction of vertex operator algebras, triality, and $E\sp {(1)}\sb 8$, Contemporary Mathematics, vol. 121, American Mathematical Society, Providence, RI, 1991.
Mathematical Reviews (MathSciNet): MR92k:17041
Zentralblatt MATH: 0743.17029
[FLM]1 I. B. Frenkel, J. Lepowsky, and A. Meurman, A natural representation of the Fischer-Griess Monster with the modular function $J$ as character, Proc. Nat. Acad. Sci. U.S.A. 81 (1984), no. 10, Phys. Sci., 3256–3260.
Mathematical Reviews (MathSciNet): MR85e:20018
Zentralblatt MATH: 0543.20016
Digital Object Identifier: doi:10.1073/pnas.81.10.3256
[FLM]2 I. Frenkel, J. Lepowsky, and A. Meurman, Vertex operator algebras and the Monster, Pure and Applied Mathematics, vol. 134, Academic Press Inc., Boston, MA, 1988.
Mathematical Reviews (MathSciNet): MR90h:17026
Zentralblatt MATH: 0674.17001
[FHL] I. B. Frenkel, Y.-Z. Huang, and J. Lepowsky, On axiomatic approaches to vertex operator algebras and modules, to appear.
Mathematical Reviews (MathSciNet): MR1142494
[G] P. Goddard, Meromorphic conformal field theory, Infinite-dimensional Lie algebras and groups (Luminy-Marseille, 1988) ed. V. G. Kac, Adv. Ser. Math. Phys., vol. 7, World Sci. Publishing, Teaneck, NJ, 1989, pp. 556–587.
Mathematical Reviews (MathSciNet): MR91f:81184
Zentralblatt MATH: 0742.17027
[GKO] P. Goddard, A. Kent, and D. Olive, Virasoro algebras and coset space models, Phys. Lett. B 152 (1985), no. 1-2, 88–92.
Mathematical Reviews (MathSciNet): MR86m:81092
Zentralblatt MATH: 0661.17015
Digital Object Identifier: doi:10.1016/0370-2693(85)91145-1
[K] V. G. Kac, Infinite-dimensional Lie algebras, and Dedekind's $\eta$-function, Funct. Anal. Appl. 8 (1974), 68–70.
Zentralblatt MATH: 0741.00064
Mathematical Reviews (MathSciNet): MR374210
[Ko] T. Kohno, Quantized universal enveloping algebras and monodromy of braid groups, Braids, Santa Cruz, 1986, Amer. Math. Soc., vol. 78, Contemp. Math., Providence, 1988.
[M] I. G. Macdonald, Affine root systems and Dedekind's $\eta$-function, Invent. Math. 15 (1972), 91–143.
Mathematical Reviews (MathSciNet): MR50:9996
Zentralblatt MATH: 0244.17005
Digital Object Identifier: doi:10.1007/BF01418931
[MS] G. Moore and N. Seiberg, Classical and quantum conformal field theory, Comm. Math. Phys. 123 (1989), no. 2, 177–254.
Mathematical Reviews (MathSciNet): MR90e:81216
Zentralblatt MATH: 0694.53074
Digital Object Identifier: doi:10.1007/BF01238857
[RT] N. Y. Reshetikhin and V. G. Turaev, Ribbon graphs and their invariants derived from quantum groups, Comm. Math. Phys. 127 (1990), no. 1, 1–26.
Mathematical Reviews (MathSciNet): MR91c:57016
Zentralblatt MATH: 0768.57003
Digital Object Identifier: doi:10.1007/BF02096491
[S] G. B. Segal, The definition of conformal field theory, Differential geometrical methods in theoretical physics (Como, 1987) eds. K. Bleuler and M. Werner, NATO Adv. Sci. Inst. Ser. C Math. Phys. Sci., vol. 250, Kluwer Acad. Publ., Dordrecht, 1988, pp. 165–171.
Mathematical Reviews (MathSciNet): MR90d:58026
Zentralblatt MATH: 0657.53060
[TK]1 A. Tsuchiya and Y. Kanie, Vertex operators in conformal field theory on ${\bf P}\sp 1$ and monodromy representations of braid group, Conformal field theory and solvable lattice models (Kyoto, 1986), Adv. Stud. Pure Math., vol. 16, Academic Press, Boston, MA, 1988, pp. 297–372.
Mathematical Reviews (MathSciNet): MR89m:81166
Zentralblatt MATH: 0661.17021
[TK]2 A. Tsuchiya and Y. Kanie, Errata to: “Vertex operators in conformal field theory on ${\bf P}\sp 1$ and monodromy representations of braid group”, Integrable systems in quantum field theory and statistical mechanics, Adv. Stud. Pure Math., vol. 19, Academic Press, Boston, MA, 1989, pp. 675–682.
Mathematical Reviews (MathSciNet): MR91h:81156
Zentralblatt MATH: 0699.17019
[TUY] A. Tsuchiya, K. Ueno, and Y. Yamada, Conformal field theory on universal family of stable curves with gauge symmetries, Integrable systems in quantum field theory and statistical mechanics eds. K. Aomoto and T. Oda, Adv. Stud. Pure Math., vol. 19, Academic Press, Boston, MA, 1989, pp. 459–566.
Mathematical Reviews (MathSciNet): MR92a:81191
Zentralblatt MATH: 0696.17010
[T] H. Tsukada, Vertex operator superalgebras, Comm. Algebra 18 (1990), no. 7, 2249–2274.
Mathematical Reviews (MathSciNet): MR92b:17034
Zentralblatt MATH: 0704.17001
[W] E. Witten, Nonabelian bosonization in two dimensions, Comm. Math. Phys. 92 (1984), no. 4, 455–472.
Mathematical Reviews (MathSciNet): MR86g:81104
Zentralblatt MATH: 0536.58012
Digital Object Identifier: doi:10.1007/BF01215276
[Z] Y. Zhu, Vertex operator algebras, elliptic functions and modular forms, Ph.D dissertation, Yale Univ., 1990.
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