메뉴 건너뛰기




Volumn 9, Issue 1, 1996, Pages 237-302

Modular invariance of characters of vertex operator algebras

Author keywords

[No Author keywords available]

Indexed keywords


EID: 0030551014     PISSN: 08940347     EISSN: None     Source Type: Journal    
DOI: 10.1090/s0894-0347-96-00182-8     Document Type: Article
Times cited : (940)

References (61)
  • 2
    • 0347612993 scopus 로고    scopus 로고
    • T.M. Apostol, Modular functions and Dirichlet series in number theory, Springer-Verlag, 1976. MR 54:10149
    • MR , vol.54 , pp. 10149
  • 3
    • 0001056693 scopus 로고
    • Vertex operator algebras, Kac-Moody algebras and the Monster
    • R.E. Borcherds, Vertex operator algebras, Kac-Moody algebras and the Monster, Proc. Natl. Acad. Sci. USA. 83 (1986), 3026. MR 87m:17033
    • (1986) Proc. Natl. Acad. Sci. USA , vol.83 , pp. 3026
    • Borcherds, R.E.1
  • 4
    • 0346981985 scopus 로고    scopus 로고
    • R.E. Borcherds, Vertex operator algebras, Kac-Moody algebras and the Monster, Proc. Natl. Acad. Sci. USA. 83 (1986), 3026. MR 87m:17033
    • MR , vol.87 M , pp. 17033
  • 5
    • 0010882054 scopus 로고    scopus 로고
    • Infinite conformal symmetry in two dimensional quantum field theory
    • 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
    • (1984) Nucl. Phys. , vol.B241 , pp. 33
    • Belavin, A.1    Polyakov, A.M.2    Zamolodchikov, A.A.3
  • 6
    • 0010882054 scopus 로고    scopus 로고
    • 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
    • MR , vol.86 M , pp. 81097
  • 7
    • 0010795998 scopus 로고    scopus 로고
    • W-symmetry in conformal field theory
    • P. Bouwknegt, K. Schoutens, W-symmetry in conformal field theory, Phys. Rep. 223 (1993). MR 94e:81096
    • (1993) Phys. Rep. , vol.223
    • Bouwknegt, P.1    Schoutens, K.2
  • 8
    • 0010795998 scopus 로고    scopus 로고
    • P. Bouwknegt, K. Schoutens, W-symmetry in conformal field theory, Phys. Rep. 223 (1993). MR 94e:81096
    • MR , vol.94 E , pp. 81096
  • 9
    • 0011402903 scopus 로고    scopus 로고
    • Operator content of two-dimensional conformal invariant theories
    • J.L. Cardy, Operator content of two-dimensional conformal invariant theories, Nucl. Phys. B270 (1986), 186. MR 87k:17017
    • (1986) Nucl. Phys. , vol.B270 , pp. 186
    • Cardy, J.L.1
  • 10
    • 0011402903 scopus 로고    scopus 로고
    • J.L. Cardy, Operator content of two-dimensional conformal invariant theories, Nucl. Phys. B270 (1986), 186. MR 87k:17017
    • MR , vol.87 K , pp. 17017
  • 12
    • 0000292099 scopus 로고    scopus 로고
    • Vertex algebras associated to even lattice
    • C. Dong, Vertex algebras associated to even lattice, J. of alg. 161 (1993). MR 94j:17023
    • (1993) J. of Alg. , vol.161
    • Dong, C.1
  • 13
    • 0000292099 scopus 로고    scopus 로고
    • C. Dong, Vertex algebras associated to even lattice, J. of alg. 161 (1993). MR 94j:17023
    • MR , vol.94 J , pp. 17023
  • 15
    • 0001276288 scopus 로고
    • Affine Kac-Moody algebras at the critical level and Gelfand-Dikii algebras
    • 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
    • (1992) Int. J. Mod. Phys. A Suppl. , vol.1 A
    • Feigin, B.1    Frenkel, E.2
  • 16
    • 0347612933 scopus 로고    scopus 로고
    • 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
    • MR , vol.93 J , pp. 17049
  • 17
    • 0001261061 scopus 로고
    • Orbital theory for affine Lie algebras
    • Yale dissertation
    • I. Frenkel, Orbital theory for affine Lie algebras, Yale dissertation (1980), or Invent. Math. 77 (1984). MR 86d:17014
    • (1980) Invent. Math. , vol.77
    • Frenkel, I.1
  • 18
    • 0348242845 scopus 로고    scopus 로고
    • I. Frenkel, Orbital theory for affine Lie algebras, Yale dissertation (1980), or Invent. Math. 77 (1984). MR 86d:17014
    • MR , vol.86 D , pp. 17014
  • 19
    • 0041125816 scopus 로고
    • W-algebras and Langlands-Drinfeld correspondence
    • (J. Frohlich, eds.), Plenum Press, New York
    • E. Frenkel, W-algebras and Langlands-Drinfeld correspondence, New Symmetries in Quantum field theory (J. Frohlich, eds.), Plenum Press, New York, 1987.
    • (1987) New Symmetries in Quantum Field Theory
    • Frenkel, E.1
  • 21
    • 0346981984 scopus 로고    scopus 로고
    • B.L. Feigin, D.B. Fuchs, Lect. Notes Math., vol 1060, 1984. MR 86g:17004
    • MR , vol.86 G , pp. 17004
  • 24
    • 0347612992 scopus 로고
    • 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
    • (1993) Memoirs American Math. Soc. , vol.104
  • 25
    • 0346352123 scopus 로고    scopus 로고
    • 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
    • MR , vol.94 A , pp. 17007
  • 26
    • 0001761027 scopus 로고
    • A natural representation of the Fischer-Griess Monster with the modular function J as a character
    • 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
    • (1984) Proc. Nat. Acad. Sci. USA , vol.81 , pp. 3256-3260
    • Frenkel, I.B.1    Lepowsky, J.2    Meurman, A.3
  • 27
    • 0348242843 scopus 로고    scopus 로고
    • 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
    • MR , vol.85 E , pp. 20018
  • 29
    • 0346352122 scopus 로고    scopus 로고
    • I.B. Frenkel, J. Lepowsky, A. Meurman, Vertex Operator Algebras and the Monster, Academic Press, New York, 1988. MR 90h:17026
    • MR , vol.90 H , pp. 17026
  • 30
    • 84973998987 scopus 로고    scopus 로고
    • Vertex operator algebras associated to representation of affine and Virasoro algebras
    • 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
    • (1992) Duke Mathematical Journal , vol.66 , pp. 123
    • Frenkel, I.B.1    Zhu, Y.2
  • 31
    • 84973998987 scopus 로고    scopus 로고
    • 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
    • MR , vol.93 G , pp. 17045
  • 32
    • 0025789737 scopus 로고    scopus 로고
    • Geometric interpretation of vertex operator algebras
    • Y.Z. Huang, Geometric interpretation of vertex operator algebras, Proc. Natl. Acad. Sci. USA 88 (1991), 9964. MR 92k:17037
    • (1991) Proc. Natl. Acad. Sci. USA , vol.88 , pp. 9964
    • Huang, Y.Z.1
  • 33
    • 0025789737 scopus 로고    scopus 로고
    • Y.Z. Huang, Geometric interpretation of vertex operator algebras, Proc. Natl. Acad. Sci. USA 88 (1991), 9964. MR 92k:17037
    • MR , vol.92 K , pp. 17037
  • 35
    • 26744463960 scopus 로고    scopus 로고
    • E.L. Ince, Ordinary Differential Equations, Dover Publications, Inc, New York, 1956. MR 6:65f
    • MR , vol.6
  • 36
    • 0000714695 scopus 로고    scopus 로고
    • Two-dimensional conformal invariant theories on a torus
    • Itsykson, Zuber, Two-dimensional conformal invariant theories on a torus, Nucl.Phys. B275 (1986). MR 88f:8111
    • (1986) Nucl.Phys. , vol.B275
    • Itsykson1    Zuber2
  • 37
    • 0000714695 scopus 로고    scopus 로고
    • Itsykson, Zuber, Two-dimensional conformal invariant theories on a torus, Nucl.Phys. B275 (1986). MR 88f:8111
    • MR , vol.88 F , pp. 8111
  • 38
    • 34250409421 scopus 로고    scopus 로고
    • Infinite dimensional Lie algebras and Dedekind's η-function
    • V.G. Kac, Infinite dimensional Lie algebras and Dedekind's η-function, Funct. Anal. Appl. 8 (1974), 68-70. MR 51:10410
    • (1974) Funct. Anal. Appl. , vol.8 , pp. 68-70
    • Kac, V.G.1
  • 39
    • 34250409421 scopus 로고    scopus 로고
    • V.G. Kac, Infinite dimensional Lie algebras and Dedekind's η-function, Funct. Anal. Appl. 8 (1974), 68-70. MR 51:10410
    • MR , vol.51 , pp. 10410
  • 40
    • 0001302993 scopus 로고    scopus 로고
    • Infinite-dimensional Lie algebras, theta functions and modular forms
    • 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
    • (1984) Advances in Math , vol.53 , pp. 124-264
    • Kac, V.G.1    Peterson, D.H.2
  • 41
    • 0001302993 scopus 로고    scopus 로고
    • 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
    • MR , vol.86 A , pp. 17007
  • 42
    • 0346981978 scopus 로고    scopus 로고
    • Modular and conformal invariance constraints in representation theory
    • V.G. Kac, M. Wakimoto, Modular and conformal invariance constraints in representation theory, Adv. Math. 70 (1988). MR 89h:17036
    • (1988) Adv. Math. , vol.70
    • Kac, V.G.1    Wakimoto, M.2
  • 43
    • 0346981978 scopus 로고    scopus 로고
    • V.G. Kac, M. Wakimoto, Modular and conformal invariance constraints in representation theory, Adv. Math. 70 (1988). MR 89h:17036
    • MR , vol.89 H , pp. 17036
  • 45
    • 0039066876 scopus 로고    scopus 로고
    • S. Lang, Elliptic Functions, Springer-Verlag, 1987. MR 88c:11028
    • MR , vol.88 C , pp. 11028
  • 47
    • 0346763470 scopus 로고    scopus 로고
    • Classical and quantum conformal field theory
    • G. Moore, N. Seiberg, Classical and quantum conformal field theory, Commun. Math. Phys. 123 (1989), 177-254. MR 90e:81216
    • (1989) Commun. Math. Phys. , vol.123 , pp. 177-254
    • Moore, G.1    Seiberg, N.2
  • 48
    • 0346763470 scopus 로고    scopus 로고
    • G. Moore, N. Seiberg, Classical and quantum conformal field theory, Commun. Math. Phys. 123 (1989), 177-254. MR 90e:81216
    • MR , vol.90 E , pp. 81216
  • 50
    • 0346981983 scopus 로고    scopus 로고
    • A. Rocha, in Vertex Operators in Mathematics and Physics, Spring-Verlag, 1983. MR 87b:17011
    • MR , vol.87 B , pp. 17011
  • 52
    • 0346981981 scopus 로고    scopus 로고
    • A. Tsuchiya, K. Ueno and Y. Yamada, in Advanced Studies on Pure Math., vol. 19, 1989, pp. 459-566. MR 92a:81191
    • MR , vol.92 A , pp. 81191
  • 53
    • 0011397631 scopus 로고
    • String path integral realization of vertex operator algebras
    • H. Tsukada, String path integral realization of vertex operator algebras, Memoirs of Amer. Math. Soc. 91,no.444 (1991). MR 91m:17044
    • (1991) Memoirs of Amer. Math. Soc. , vol.91 , Issue.444
    • Tsukada, H.1
  • 54
    • 0346352125 scopus 로고    scopus 로고
    • H. Tsukada, String path integral realization of vertex operator algebras, Memoirs of Amer. Math. Soc. 91,no.444 (1991). MR 91m:17044
    • MR , vol.91 M , pp. 17044
  • 56
    • 0347612990 scopus 로고    scopus 로고
    • N.R. Wallach, Real Reductive Groups I, Academic Press, 1988. MR 89i:22029
    • MR , vol.89 I , pp. 22029
  • 57
    • 84963036993 scopus 로고    scopus 로고
    • Rationality of Virasoro vertex operator algebras
    • W. Wang, Rationality of Virasoro vertex operator algebras, Duke Math. J., IMRN 71, No. 1 (1993). MR 94i:17034
    • (1993) Duke Math. J., IMRN , vol.71 , Issue.1
    • Wang, W.1
  • 58
    • 84963036993 scopus 로고    scopus 로고
    • W. Wang, Rationality of Virasoro vertex operator algebras, Duke Math. J., IMRN 71, No. 1 (1993). MR 94i:17034
    • MR , vol.94 I , pp. 17034
  • 59
    • 0000725723 scopus 로고    scopus 로고
    • Quantum field theory, Grassmannians, and algebraic curves
    • E. Witten, Quantum field theory, Grassmannians, and algebraic curves, Commun. Math. Phys. 113 (1988), 529-600. MR 88m:81127
    • (1988) Commun. Math. Phys. , vol.113 , pp. 529-600
    • Witten, E.1
  • 60
    • 0000725723 scopus 로고    scopus 로고
    • E. Witten, Quantum field theory, Grassmannians, and algebraic curves, Commun. Math. Phys. 113 (1988), 529-600. MR 88m:81127
    • MR , vol.88 M , pp. 81127
  • 61
    • 21844525983 scopus 로고
    • Global vertex operators on Riemann surfaces
    • Y. Zhu, Global vertex operators on Riemann surfaces, Commun. Math. Phys. 165 No.3 (1994).
    • (1994) Commun. Math. Phys. , vol.165 , Issue.3
    • Zhu, Y.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.