메뉴 건너뛰기




Volumn 85, Issue 2, 1996, Pages 447-510

Representation theory of Chern-Simons observables

Author keywords

[No Author keywords available]

Indexed keywords


EID: 0000480877     PISSN: 00127094     EISSN: None     Source Type: Journal    
DOI: 10.1215/S0012-7094-96-08519-1     Document Type: Article
Times cited : (68)

References (51)
  • 1
    • 0042754157 scopus 로고
    • Integrability in the Hamiltonian Chern-Simons theory
    • A. YU. ALEKSEEV, Integrability in the Hamiltonian Chern-Simons theory, St. Petersburg Math. J. 6, 2 (1994), 241-253.
    • (1994) St. Petersburg Math. J. , vol.6 , Issue.2 , pp. 241-253
    • Alekseev, A.Yu.1
  • 3
    • 0039902474 scopus 로고
    • Combinatorial quantization of the Hamiltonian Chern-Simons theory I
    • A. YU. ALEKSEEV, H. GROSSE, AND V. SCHOMERUS, Combinatorial quantization of the Hamiltonian Chern-Simons theory I, Comm. Math. Phys. 172 (1995), 317-358.
    • (1995) Comm. Math. Phys. , vol.172 , pp. 317-358
    • Alekseev, A.Yu.1    Grosse, H.2    Schomerus, V.3
  • 4
    • 0030542947 scopus 로고    scopus 로고
    • Combinatorial quantization of the Hamiltonian Chern-Simons theory II
    • _, Combinatorial quantization of the Hamiltonian Chern-Simons theory II, Comm. Math. Phys. 174 (1996), 561-604.
    • (1996) Comm. Math. Phys. , vol.174 , pp. 561-604
  • 6
    • 21144484691 scopus 로고
    • Quasi-quantum groups, knots, three-manifolds, and topological field theory
    • D. ALTSCHULER AND A. COSTE, Quasi-quantum groups, knots, three-manifolds, and topological field theory, Comm. Math. Phys. 150 (1992), 83-107.
    • (1992) Comm. Math. Phys. , vol.150 , pp. 83-107
    • Altschuler, D.1    Coste, A.2
  • 8
    • 0011635385 scopus 로고    scopus 로고
    • in preparation
    • J. ANDERSEN, J. MATTES, AND N. RESHETIKHIN, Poisson structure on the moduli space of flat connections and chord diagrams, preprint, Aarhus, 1995; Quantization of the algebra of chord diagrams, in preparation.
    • Quantization of the Algebra of Chord Diagrams
  • 10
  • 11
    • 84972540587 scopus 로고
    • Chern-Simons perturbation theory II
    • S. AXELROD AND I. M. SINGER, Chern-Simons perturbation theory II, J. Differential Geom. 39 (1994), 173-213.
    • (1994) J. Differential Geom. , vol.39 , pp. 173-213
    • Axelrod, S.1    Singer, I.M.2
  • 12
    • 0000300789 scopus 로고
    • q-deformed lattice gauge theory and 3-manifold invariants
    • D. V. BOULATOV, q-deformed lattice gauge theory and 3-manifold invariants, Internat. J. Modern Phys. A 8 (1993), 3139-3162.
    • (1993) Internat. J. Modern Phys. A , vol.8 , pp. 3139-3162
    • Boulatov, D.V.1
  • 13
    • 21844475730 scopus 로고
    • Two-dimensional lattice gauge theory based on a quantum group
    • E. BUFFENOIR AND PH. ROCHE, Two-dimensional lattice gauge theory based on a quantum group, Comm. Math. Phys. 170 (1995), 669-698.
    • (1995) Comm. Math. Phys. , vol.170 , pp. 669-698
    • Buffenoir, E.1    Roche, Ph.2
  • 14
    • 0001334959 scopus 로고
    • Representations of quantum groups at roots of 1
    • Operator Algebras, Unitary Representations, Enveloping Algebras, and Invariant Theory, Birkhäuser, Boston
    • C. DE CONCINI AND V. KAC, "Representations of quantum groups at roots of 1" in Operator Algebras, Unitary Representations, Enveloping Algebras, and Invariant Theory, Progr. Math. 92, Birkhäuser, Boston, 1990, 471-506.
    • (1990) Progr. Math. , vol.92 , pp. 471-506
    • De Concini, C.1    Kac, V.2
  • 16
    • 0006872661 scopus 로고
    • Quasi-hopf algebras and Knizhnik-Zamolodchikov equations
    • Res. Rep. Phys., Springer-Verlag, Berlin
    • _, ̈Quasi-Hopf algebras and Knizhnik-Zamolodchikov equations̈ in Problems of Modern Quantum Field Theory (Alushta, 1989), Res. Rep. Phys., Springer-Verlag, Berlin, 1989, 1-13; Quasi-Hopf algebras, Leningrad. Math. J. 1 (1990), 1419-1457.
    • (1989) Problems of Modern Quantum Field Theory (Alushta, 1989) , pp. 1-13
  • 17
    • 0000805003 scopus 로고
    • Quasi-Hopf algebras
    • _, ̈Quasi-Hopf algebras and Knizhnik-Zamolodchikov equations̈ in Problems of Modern Quantum Field Theory (Alushta, 1989), Res. Rep. Phys., Springer-Verlag, Berlin, 1989, 1-13; Quasi-Hopf algebras, Leningrad. Math. J. 1 (1990), 1419-1457.
    • (1990) Leningrad. Math. J. , vol.1 , pp. 1419-1457
  • 18
    • 0000308394 scopus 로고
    • A construction of topological quantum field theories from 6j-symbols
    • B. DURHUUS, H. P. JAKOBSEN, AND R. NEST, A construction of topological quantum field theories from 6j-symbols, Nuclear Phys. B Proc. Suppl. 25A (1992), 109-121.
    • (1992) Nuclear Phys. B Proc. Suppl. , vol.25 A , pp. 109-121
    • Durhuus, B.1    Jakobsen, H.P.2    Nest, R.3
  • 19
    • 33744524965 scopus 로고
    • Remarks on the canonical quantization of the Chern-Simons-Witten theory
    • S. ELITZUR, G. MOORE, A. SCHWIMMER, AND N. SEIBERG, Remarks on the canonical quantization of the Chern-Simons-Witten theory, Nuclear Phys. B 326 (1989), 108-134.
    • (1989) Nuclear Phys. B , vol.326 , pp. 108-134
    • Elitzur, S.1    Moore, G.2    Schwimmer, A.3    Seiberg, N.4
  • 20
    • 0000833744 scopus 로고
    • Quantization of Lie Groups and Lie Algebras
    • Academic Press, Boston
    • L. D. FADDEEV, N. YU. RESHETIKHIN, L. A. TAKHTADZHYAN, "Quantization of Lie Groups and Lie Algebras" in Algebraic Analysis, Vol. 1, Academic Press, Boston, 1988, 129-139; English transl, in Leningrad Math. J. 1 (1990), 193-225.
    • (1988) Algebraic Analysis , vol.1 , pp. 129-139
    • Faddeev, L.D.1    Reshetikhin, N.Yu.2    Takhtadzhyan, L.A.3
  • 21
    • 0000057580 scopus 로고
    • English transl
    • L. D. FADDEEV, N. YU. RESHETIKHIN, L. A. TAKHTADZHYAN, "Quantization of Lie Groups and Lie Algebras" in Algebraic Analysis, Vol. 1, Academic Press, Boston, 1988, 129-139; English transl, in Leningrad Math. J. 1 (1990), 193-225.
    • (1990) Leningrad Math. J. , vol.1 , pp. 193-225
  • 23
    • 84972506966 scopus 로고
    • A simple geometrical construction of deformation quantization
    • B. V. FEDOSOV, "Formal quantization" in Some Problems in Modern Mathematics and Their Application to Problems in Mathematical Physics, Moskow Fiz. Tekhn. Inst., Moscow, 1985, 129-136; A simple geometrical construction of deformation quantization, J. Differential Geom. 40 (1994), 213-238.
    • (1994) J. Differential Geom. , vol.40 , pp. 213-238
  • 26
    • 0000253059 scopus 로고
    • Braid statistics in local quantum theory
    • J. FRÖHLICH AND F. GABBIANI, Braid statistics in local quantum theory, Rev. Math. Phys. 2 (1990), 251-353.
    • (1990) Rev. Math. Phys. , vol.2 , pp. 251-353
    • Fröhlich, J.1    Gabbiani, F.2
  • 27
    • 0000086776 scopus 로고
    • Invariant functions on Lie groups and Hamiltonian flows of surface group representations
    • W. GOLDMAN, Invariant functions on Lie groups and Hamiltonian flows of surface group representations, Invent. Math. 85 (1986) 263-302; The symplectic nature of fundamental groups of surfaces, Adv. Math. 54 (1984), 200-225.
    • (1986) Invent. Math. , vol.85 , pp. 263-302
    • Goldman, W.1
  • 28
    • 0001360773 scopus 로고
    • The symplectic nature of fundamental groups of surfaces
    • W. GOLDMAN, Invariant functions on Lie groups and Hamiltonian flows of surface group representations, Invent. Math. 85 (1986) 263-302; The symplectic nature of fundamental groups of surfaces, Adv. Math. 54 (1984), 200-225.
    • (1984) Adv. Math. , vol.54 , pp. 200-225
  • 30
    • 0039743786 scopus 로고
    • talk given at Newton Institute, Cambridge, November
    • L. JEFFREY AND F. KIRWAN, talk given at Newton Institute, Cambridge, November 1994.
    • (1994)
    • Jeffrey, L.1    Kirwan, F.2
  • 31
    • 21144473653 scopus 로고
    • A combinatorial approach to topological quantum field theories and invariants of graphs
    • M. KAROWSKI AND R. SCHRADER, A combinatorial approach to topological quantum field theories and invariants of graphs, Comm. Math. Phys. 151 (1993), 355-402; A quantum group version of quantum gauge theories in two dimensions, J. Phys. A 25 (1992), L1151-L1154.
    • (1993) Comm. Math. Phys. , vol.151 , pp. 355-402
    • Karowski, M.1    Schrader, R.2
  • 32
    • 21144465288 scopus 로고
    • A quantum group version of quantum gauge theories in two dimensions
    • M. KAROWSKI AND R. SCHRADER, A combinatorial approach to topological quantum field theories and invariants of graphs, Comm. Math. Phys. 151 (1993), 355-402; A quantum group version of quantum gauge theories in two dimensions, J. Phys. A 25 (1992), L1151-L1154.
    • (1992) J. Phys. A , vol.25
  • 33
    • 84968466254 scopus 로고
    • Tensor structures arising from affine Lie algebras, I, II
    • D. KAZHDAN AND G. LUSZTIG, Tensor structures arising from affine Lie algebras, I, II, J. Amer. Math. Soc. 6 (1993), 905-947, 949-1011.
    • (1993) J. Amer. Math. Soc. , vol.6 , pp. 905-947
    • Kazhdan, D.1    Lusztig, G.2
  • 34
    • 0039131275 scopus 로고
    • Mapping class group actions on quantum doubles
    • T. KERLER, Mapping class group actions on quantum doubles, Comm. Math. Phys. 168 (1995), 353-388.
    • (1995) Comm. Math. Phys. , vol.168 , pp. 353-388
    • Kerler, T.1
  • 36
    • 33744774508 scopus 로고
    • Current algebra and Wess-Zumino model in two dimensions
    • V. KNIZHNIK AND A. B. ZAMOLODCHIKOV, Current algebra and Wess-Zumino model in two dimensions, Nuclear Phys. B 247 (1984), 83-103.
    • (1984) Nuclear Phys. B , vol.247 , pp. 83-103
    • Knizhnik, V.1    Zamolodchikov, A.B.2
  • 37
    • 84968491405 scopus 로고
    • Finite-dimensional Hopf algebras arising from quantized universal enveloping algebra
    • G. LUSZTIG, Finite-dimensional Hopf algebras arising from quantized universal enveloping algebra, J. Amer. Math. Soc. 3 (1990), 257-296.
    • (1990) J. Amer. Math. Soc. , vol.3 , pp. 257-296
    • Lusztig, G.1
  • 38
    • 0000554574 scopus 로고
    • Tangles and Hopf algebras in braided tensor categories
    • V. LYUBASHENKO, Tangles and Hopf algebras in braided tensor categories, J. Pure Appl. Algebra 98 (1995), 245-278.
    • (1995) J. Pure Appl. Algebra , vol.98 , pp. 245-278
    • Lyubashenko, V.1
  • 39
    • 0011694830 scopus 로고
    • Quasi Hopf quantum symmetry in quantum theory
    • G. MACK AND V. SCHOMERUS, Quasi Hopf quantum symmetry in quantum theory, Nuclear Phys. B 370 (1992), 185-230.
    • (1992) Nuclear Phys. B , vol.370 , pp. 185-230
    • Mack, G.1    Schomerus, V.2
  • 40
    • 0346405348 scopus 로고
    • Braided groups
    • S. MAJID, Braided groups, J. Pure Appl. Algebra 86 (1993), 187-221; "Algebras and Hopf algebras in braided categories" in Advances in Hopf Algebras, Lecture Notes in Pure and Appl. Math. 158, Dekker, New York, 1994, 55-105.
    • (1993) J. Pure Appl. Algebra , vol.86 , pp. 187-221
    • Majid, S.1
  • 41
    • 0346405348 scopus 로고
    • Algebras and Hopf algebras in braided categories
    • Advances in Hopf Algebras, Dekker, New York
    • S. MAJID, Braided groups, J. Pure Appl. Algebra 86 (1993), 187-221; "Algebras and Hopf algebras in braided categories" in Advances in Hopf Algebras, Lecture Notes in Pure and Appl. Math. 158, Dekker, New York, 1994, 55-105.
    • (1994) Lecture Notes in Pure and Appl. Math. , vol.158 , pp. 55-105
  • 42
    • 21344492904 scopus 로고
    • A geometrical presentation of the surface mapping class group and surgery
    • S. MATVEEV AND M. POLYAK, A geometrical presentation of the surface mapping class group and surgery, Comm. Math. Phys. 160 (1994), 537-550.
    • (1994) Comm. Math. Phys. , vol.160 , pp. 537-550
    • Matveev, S.1    Polyak, M.2
  • 44
    • 34249960869 scopus 로고
    • Ribbon graphs and their invariants derived from quantum groups
    • N. RESHETIKHIN AND V. G. TURAEV, Ribbon graphs and their invariants derived from quantum groups, Comm. Math. Phys. 127 (1990), 1-26.
    • (1990) Comm. Math. Phys. , vol.127 , pp. 1-26
    • Reshetikhin, N.1    Turaev, V.G.2
  • 45
    • 0542373499 scopus 로고
    • Invariants of 3-manifolds via link polynomials and quantum groups
    • _, Invariants of 3-manifolds via link polynomials and quantum groups, Invent. Math. 103 (1991), 547-597.
    • (1991) Invent. Math. , vol.103 , pp. 547-597
  • 46
    • 0002355820 scopus 로고
    • Non-commuting coordinates and differential operators
    • ed. by T. Curtright et al., World Scientific, Singapore
    • A. SUDBURY, "Non-commuting coordinates and differential operators" in Proceedings of the Argonne Workshop, Quantum Groups; ed. by T. Curtright et al., World Scientific, Singapore, 1991; 33-52.
    • (1991) Proceedings of the Argonne Workshop, Quantum Groups , pp. 33-52
    • Sudbury, A.1
  • 47
    • 0007227751 scopus 로고
    • Skein quantization of Poisson algebras of loops on surfaces
    • V. TURAEV, Skein quantization of Poisson algebras of loops on surfaces, Ann. Sci. Ecole Norm. Sup. (4) 24 (1991), 635-704.
    • (1991) Ann. Sci. Ecole Norm. Sup. , vol.24 , Issue.4 , pp. 635-704
    • Turaev, V.1
  • 48
    • 44049114062 scopus 로고
    • State sum of 3-manifolds and quantum 6j-symbols
    • V. G. TURAEV AND O. Y. VIRO, State sum of 3-manifolds and quantum 6j-symbols, Topology 31 (1992), 865-902.
    • (1992) Topology , vol.31 , pp. 865-902
    • Turaev, V.G.1    Viro, O.Y.2
  • 49
    • 45549111952 scopus 로고
    • Fusion rules and modular transformations in 2D conformal field theory
    • E. VERLINDE, Fusion rules and modular transformations in 2D conformal field theory, Nuclear Phys. B 300 (1988), 360-376.
    • (1988) Nuclear Phys. B , vol.300 , pp. 360-376
    • Verlinde, E.1
  • 50
    • 14644388676 scopus 로고
    • Quantum field theory and the Jones polynomial
    • E. WITTEN, Quantum field theory and the Jones polynomial, Comm. Math. Phys. 121 (1989), 351-399.
    • (1989) Comm. Math. Phys. , vol.121 , pp. 351-399
    • Witten, E.1
  • 51
    • 17144427930 scopus 로고
    • Two-dimensional gauge theories revisited
    • _, Two-dimensional gauge theories revisited, J. Geom. Phys. 9 (1992), 303-368.
    • (1992) J. Geom. Phys. , vol.9 , pp. 303-368


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.