Intertwining operator algebras and vertex tensor categories for affine Lie algebras
Yi-Zhi Huang and James Lepowsky
Source: Duke Math. J. Volume 99, Number 1
(1999), 113-134.
First Page:
Show
Hide
Full-text: Access denied (no subscription
detected)
We're sorry, but we are unable to provide
you with the full text of this article because we are not able to identify
you as a subscriber.
If you have a personal subscription to
this journal, then please login. If you are already logged in, then you
may need to update your profile to register your subscription. Read more about accessing full-text
Links and Identifiers
Permanent link to this document: http://projecteuclid.org/euclid.dmj/1077227633
Mathematical Reviews number (MathSciNet): MR1700743
Zentralblatt MATH identifier: 0953.17016
Digital Object Identifier: doi:10.1215/S0012-7094-99-09905-2
References
[BFM] A. Beilinson, B. Feigin, and B. Mazur, Introduction to algebraic field theory on curves, preprint, (provided by A. Beilinson, 1996), 1991.
[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] Richard 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
JSTOR: links.jstor.org
[De] P. Deligne, Une description de catégorie tressée (inspiré par Drinfeld), unpublished.
[DL] Chongying Dong and James Lepowsky, Generalized vertex algebras and relative vertex operators, Progress in Mathematics, vol. 112, Birkhäuser Boston Inc., Boston, MA, 1993.
Mathematical Reviews (MathSciNet): MR95b:17032
Zentralblatt MATH: 0803.17009
[DLM] Chongying Dong, Haisheng Li, and Geoffrey Mason, Regularity of rational vertex operator algebras, Adv. Math. 132 (1997), no. 1, 148–166.
Mathematical Reviews (MathSciNet): MR98m:17037
Zentralblatt MATH: 0902.17014
Digital Object Identifier: doi:10.1006/aima.1997.1681
[DM] Chongying Dong and Geoffrey Mason, On quantum Galois theory, Duke Math. J. 86 (1997), no. 2, 305–321.
Mathematical Reviews (MathSciNet): MR97k:17042
Zentralblatt MATH: 0890.17031
Digital Object Identifier: doi:10.1215/S0012-7094-97-08609-9
Project Euclid: euclid.dmj/1077242668
[DMZ] Chongying Dong, Geoffrey Mason, and Yongchang Zhu, Discrete series of the Virasoro algebra and the moonshine module, Algebraic groups and their generalizations: quantum and infinite-dimensional methods (University Park, PA, 1991), Proc. Sympos. Pure Math., vol. 56, Amer. Math. Soc., Providence, RI, 1994, pp. 295–316.
Mathematical Reviews (MathSciNet): MR95c:17043
Zentralblatt MATH: 0813.17019
[Dr] V. G. Drinfeld, On quasitriangular quasi-Hopf algebras and on a group that is closely connected with $\rm Gal(\overline\bf Q/\bf Q)$, Algebra i Analiz 2 (1990), no. 4, 149–181, (in Russian); English transl. in Leningrad Math. J. 2 (1991), 829–860.
Mathematical Reviews (MathSciNet): MR92f:16047
Zentralblatt MATH: 0728.16021
[F1] M. Finkelberg, Fusion categories, Ph.D. thesis, Harvard University, 1993.
[F2] M. Finkelberg, An equivalence of fusion categories, Geom. Funct. Anal. 6 (1996), no. 2, 249–267.
Mathematical Reviews (MathSciNet): MR97d:17015
Zentralblatt MATH: 0860.17040
Digital Object Identifier: doi:10.1007/BF02247887
[FHL] I. B. Frenkel, Y.-Z. Huang, and J. Lepowsky, On axiomatic approaches to vertex operator algebras and modules, Mem. Amer. Math. Soc. 104, Amer. Math. Soc., Providence, 1993 no. 494 (preprint, 1989).
Mathematical Reviews (MathSciNet): MR1142494
Zentralblatt MATH: 0789.17022
[FLM] Igor Frenkel, James Lepowsky, and Arne 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
[FZ] Igor B. Frenkel and Yongchang Zhu, Vertex operator algebras associated to representations of affine and Virasoro algebras, Duke Math. J. 66 (1992), no. 1, 123–168.
Mathematical Reviews (MathSciNet): MR93g:17045
Zentralblatt MATH: 0848.17032
Digital Object Identifier: doi:10.1215/S0012-7094-92-06604-X
Project Euclid: euclid.dmj/1077294666
[H1] Yi-Zhi Huang, A theory of tensor products for module categories for a vertex operator algebra. IV, J. Pure Appl. Algebra 100 (1995), no. 1-3, 173–216.
Mathematical Reviews (MathSciNet): MR98a:17050
Zentralblatt MATH: 0841.17015
Digital Object Identifier: doi:10.1016/0022-4049(95)00050-7
[H2] Yi-Zhi Huang, Virasoro vertex operator algebras, the (nonmeromorphic) operator product expansion and the tensor product theory, J. Algebra 182 (1996), no. 1, 201–234.
Mathematical Reviews (MathSciNet): MR97h:17029
Zentralblatt MATH: 0862.17022
Digital Object Identifier: doi:10.1006/jabr.1996.0168
[H3] Yi-Zhi Huang, Intertwining operator algebras, genus-zero modular functors and genus-zero conformal field theories, Operads: Proceedings of Renaissance Conferences (Hartford, CT/Luminy, 1995), Contemp. Math., vol. 202, Amer. Math. Soc., Providence, RI, 1997, pp. 335–355.
Mathematical Reviews (MathSciNet): MR98a:17051
Zentralblatt MATH: 0871.17022
[H4] Yi-Zhi Huang, Two-dimensional conformal geometry and vertex operator algebras, Progress in Mathematics, vol. 148, Birkhäuser Boston Inc., Boston, MA, 1997.
Mathematical Reviews (MathSciNet): MR98i:17037
Zentralblatt MATH: 0884.17021
[H5] Yi-Zhi Huang, Genus-zero modular functors and intertwining operator algebras, Internat. J. Math. 9 (1998), no. 7, 845–863.
Mathematical Reviews (MathSciNet): MR99i:17031
Zentralblatt MATH: 0918.17022
Digital Object Identifier: doi:10.1142/S0129167X9800035X
[H6] Y.-Z. Huang, Generalized rationality and a generalized Jacobi identity for intertwining operator algebras, to appear in Selecta Math. (N.S.).
Mathematical Reviews (MathSciNet): MR1817614
Zentralblatt MATH: 1013.17026
Digital Object Identifier: doi:10.1007/PL00001389
[HL1] Yi-Zhi Huang and James Lepowsky, Toward a theory of tensor products for representations of a vertex operator algebra, Proceedings of the XXth International Conference on Differential Geometric Methods in Theoretical Physics, Vol. 1, 2 (New York, 1991), World Sci. Publishing, River Edge, NJ, 1992, pp. 344–354.
Mathematical Reviews (MathSciNet): MR94k:17045
Zentralblatt MATH: 0829.17025
[HL2] Yi-Zhi Huang and James Lepowsky, Tensor products of modules for a vertex operator algebra and vertex tensor categories, Lie theory and geometry, Progr. Math., vol. 123, Birkhäuser Boston, Boston, MA, 1994, pp. 349–383.
Mathematical Reviews (MathSciNet): MR96e:17061
Zentralblatt MATH: 0848.17031
[HL3] Y.-Z. Huang and J. Lepowsky, A theory of tensor products for module categories for a vertex operator algebra. I, Selecta Math. (N.S.) 1 (1995), no. 4, 699–756.
Mathematical Reviews (MathSciNet): MR98a:17047
Zentralblatt MATH: 0854.17032
Digital Object Identifier: doi:10.1007/BF01587908
[HL4] Y.-Z. Huang and J. Lepowsky, A theory of tensor products for module categories for a vertex operator algebra. II, Selecta Math. (N.S.) 1 (1995), no. 4, 757–786.
Mathematical Reviews (MathSciNet): MR98a:17047
Zentralblatt MATH: 0854.17033
Digital Object Identifier: doi:10.1007/BF01587908
[HL5] Yi-Zhi Huang and James Lepowsky, A theory of tensor products for module categories for a vertex operator algebra. III, J. Pure Appl. Algebra 100 (1995), no. 1-3, 141–171.
Mathematical Reviews (MathSciNet): MR98a:17049
Zentralblatt MATH: 0841.17014
Digital Object Identifier: doi:10.1016/0022-4049(95)00049-3
[HL6] Y.-Z. Huang and J. Lepowsky, A theory of tensor products for module categories for a vertex operator algebra, V, to appear.
[JS] A. Joyal and R. Street, Braided monoidal categories, preprint, Macquarie University, Sydney, Australia, 1986.
[KL1] David Kazhdan and George Lusztig, Affine Lie algebras and quantum groups, Internat. Math. Res. Notices (1991), no. 2, 21–29.
Mathematical Reviews (MathSciNet): MR92g:17015
Zentralblatt MATH: 0726.17015
Digital Object Identifier: doi:10.1155/S1073792891000041
[KL2] D. Kazhdan and G. Lusztig, Tensor structures arising from affine Lie algebras. I, J. Amer. Math. Soc. 6 (1993), no. 4, 905–947.
Mathematical Reviews (MathSciNet): MR93m:17014
Zentralblatt MATH: 0786.17017
Digital Object Identifier: doi:10.2307/2152745
JSTOR: links.jstor.org
[KL3] D. Kazhdan and G. Lusztig, Tensor structures arising from affine Lie algebras.II, J. Amer. Math. Soc. 6 (1993), no. 4, 949–1011.
Mathematical Reviews (MathSciNet): MR93m:17014
Zentralblatt MATH: 0786.17017
Digital Object Identifier: doi:10.2307/2152745
JSTOR: links.jstor.org
[KL4] D. Kazhdan and G. Lusztig, Tensor structures arising from affine Lie algebras. III, J. Amer. Math. Soc. 7 (1994), no. 2, 335–381.
Mathematical Reviews (MathSciNet): MR94g:17048
Zentralblatt MATH: 0802.17007
Digital Object Identifier: doi:10.2307/2152762
JSTOR: links.jstor.org
[KL5] D. Kazhdan and G. Lusztig, Tensor structures arising from affine Lie algebras. IV, J. Amer. Math. Soc. 7 (1994), no. 2, 383–453.
Mathematical Reviews (MathSciNet): MR94g:17049
Zentralblatt MATH: 0802.17008
Digital Object Identifier: doi:10.2307/2152763
JSTOR: links.jstor.org
[K] Anthony W. Knapp, Representation theory of semisimple groups, Princeton Mathematical Series, vol. 36, Princeton University Press, Princeton, NJ, 1986, An Overview Based on Examples.
Mathematical Reviews (MathSciNet): MR87j:22022
Zentralblatt MATH: 0604.22001
[KZ] V. G. Knizhnik and A. B. Zamolodchikov, Current algebra and Wess-Zumino model in two dimensions, Nuclear Phys. B 247 (1984), no. 1, 83–103.
Mathematical Reviews (MathSciNet): MR87h:81129
Digital Object Identifier: doi:10.1016/0550-3213(84)90374-2
[L1] H. Li, Representation theory and the tensor product theory for vertex operator algebras, Ph.D. thesis, Rutgers University, 1994.
[L2] Hai-Sheng Li, Local systems of vertex operators, vertex superalgebras and modules, J. Pure Appl. Algebra 109 (1996), no. 2, 143–195.
Mathematical Reviews (MathSciNet): MR97d:17016
Zentralblatt MATH: 0854.17035
Digital Object Identifier: doi:10.1016/0022-4049(95)00079-8
[L3] Haisheng Li, An analogue of the Hom functor and a generalized nuclear democracy theorem, Duke Math. J. 93 (1998), no. 1, 73–114.
Mathematical Reviews (MathSciNet): MR99d:17031
Zentralblatt MATH: 0956.17017
Digital Object Identifier: doi:10.1215/S0012-7094-98-09303-6
Project Euclid: euclid.dmj/1077230637
[MS] Gregory Moore and Nathan 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
Project Euclid: euclid.cmp/1104178762
[S1] G. B. Segal, The definition of conformal field theory, preprint, 1988.
Mathematical Reviews (MathSciNet): MR981378
Zentralblatt MATH: 0657.53060
[S2] Graeme Segal, Two-dimensional conformal field theories and modular functors, IXth International Congress on Mathematical Physics (Swansea, 1988), Hilger, Bristol, 1989, pp. 22–37.
Mathematical Reviews (MathSciNet): MR92b:81192
[TK]1 Akihiro Tsuchiya and Yukihiro 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] Akihiro Tsuchiya, Kenji Ueno, and Yasuhiko Yamada, Conformal field theory on universal family of stable curves with gauge symmetries, Integrable systems in quantum field theory and statistical mechanics, Adv. Stud. Pure Math., vol. 19, Academic Press, Boston, MA, 1989, pp. 459–566.
Mathematical Reviews (MathSciNet): MR92a:81191
Zentralblatt MATH: 0696.17010
[Va] A. Varchenko, Multidimensional hypergeometric functions and representation theory of Lie algebras and quantum groups, Advanced Series in Mathematical Physics, vol. 21, World Scientific Publishing Co. Inc., River Edge, NJ, 1995.
Mathematical Reviews (MathSciNet): MR99i:32029
Zentralblatt MATH: 0951.33001
[Ve] Erik Verlinde, Fusion rules and modular transformations in $2$D conformal field theory, Nuclear Phys. B 300 (1988), no. 3, 360–376.
Mathematical Reviews (MathSciNet): MR89h:81238
Digital Object Identifier: doi:10.1016/0550-3213(88)90603-7
Duke Mathematical Journal