Operator algebras and conformal field theory III. Fusion of positive energy representations of LSU(N) using bounded operators

Inventiones Mathematicae

Volumn 133, Issue 3, 1998, Pages 467-538

  Wassermann, Antony ^a  

^a UNIVERSITY OF CAMBRIDGE   (United Kingdom)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0032344404     PISSN: 00209910     EISSN: None     Source Type: Journal    
DOI: 10.1007/s002220050253     Document Type: Article

References (49)

1. H. Araki, von Neumann algebras of local observables for free scalar field, J. Math. Phys. 5, 1-13. (1964)
2. H. Araki, On quasi-free states of CAR and Bogoliubov automorphisms, Publ. R.I.M.S. 6,385-442 (1970)
3. J. Baez, I. Segal and Z. Zhou, "Introduction to algebraic and constructive quantum field theory", Princeton University Press 1992
4. J. Bisognano and E. Wichmann, On the duality condition for a hermitian scalar field, J. Math. Phys. 16, 985-1007 (1975)
5. R. Borcherds, Vertex algebras, Kac-Moody algebras and the Monster, Proc. Nat. Acad. Sci. U.S.A. 83, 3068-3071 (1986)
6. H. Borchers, A remark on a theorem of Misra, Commun. Math. Phys. 4, 315-323 (1967)
7. H. Borchers, The CPT theorem in two-dimensional theories of local observables, Commun. Math. Phys. 143, 315-323 (1992)
8. O. Bratteli and D. Robinson, "Operator algebras and quantum statistical mechanics", Vol. I, Springer 1979
9. A. Connes, "Non-commutative geometry" (Chapter V, Appendix B), Academic Press 1994
10. S. Doplicher, R. Haag and J. Roberts, Local observables and particle statistics I, II, Comm. Math. Phys. 23 (1971) 119-230 and 35, 49-85 (1974)
11. S. Doplicher, R. Haag and J. Roberts, Local observables and particle statistics I, II, Comm. Math. Phys. 23 (1971) 119-230 and 35, 49-85 (1974)
12. J. Glimm and A. Jaffe, "Quantum Physics", 2nd edition, Springer-Verlag 1987
13. P. Goddard and D. Olive, eds., "Kac-Moody and Virasoro algebras", Advanced Series in Math. Physics Vol. 3, World Scientific 1988
14. R. Goodman and N. Wallach, Structure and unitary cocycle representations of loop groups and the group of diffeomorphisms of the circle, J. Reine Angew. Math 347, 69-133 (1984)
15. F. Goodman and H. Wenzl, Littlewood Richardson coefficients for Hecke algebras at roots of unity. Adv. Math. 82, 244-265 (1990)
16. R. Haag, "Local quantum physics", Springer-Verlag 1992.
17. N. Hugenholtz and J. Wierenga, On locally normal states in quantum statistical mechanics, Commun. Math. Phys. 11 (1969), 183-197
18. E. Ince, "Ordinary differential equations", Dover 1956
19. V. Jones. Index for subfactors, Invent, math. 72, 1-25 (1983)
20. V. Jones, von Neumann algebras in mathematics and physics, Proc. I.C.M. Kyoto 1990, 121-138
21. R. Jost, "The general theory of quantised fields", A.M.S. 1965
22. V. Kac, "Infinite dimensional Lie algebras", 3rd edition, C.U.P. 1990
23. D. Kazhdan and G. Lusztig, Tensor structures arising from affine Lie algebras IV, Journal A.M.S. 7 (1994), 383-453
24. V. Knizhnik and A. Zamolodchikov, Current algebra and Wess-Zumino models in two dimensions, Nuc. Phys. B 247, 83-103 (1984)
25. P. Leyland, J. Roberts and D. Testard, Duality for quantum free fields, preprint, Luminy 1978
26. 1", thesis, Cambridge 1994
27. F. Murray and J. von Neumann, On rings of operators, Ann. Math. 37 (1936), 116-229.
28. T. Nakanishi and A. Tsuchiya. Level-rank duality of WZW models in conformal field theory, Comm. Math. Phys. 144, 351-372 (1992)
29. E. Nelson, "Topics in dynamics I: Flows", Princeton University Press 1969
30. S. Popa, "Classification of subfactors and their endomorphisms", C.B.M.S. lectures, A.M.S. 1995
31. A. Pressley and G. Segal, "Loop groups", O.U.P. 1986
32. M. Reed and B. Simon, "Methods of Mathematical Physics I: Functional analysis", Academic Press 1980
33. H. Reeh and S. Schlieder, Bemerkungen zur Unitarequivalenz von Lorentzinvarienten Feldern, Nuovo Cimento 22, 1051-1068 (1961)
34. M. Rieffel and A. van Daele, A bounded operator approach to Tomita-Takesaki theory, Pacific J. Math. 69, 187-221 (1977)
35. J.-L. Sauvageot, Sur le produit tensoriel relatif d'espaces d'Hilbert, J. Op. Theory 9, 237-252
36. G. Segal, Notes on conformal field theory, unpublished manuscript
37. R. Streater and A. Wightman, "PCT, spin statistics and all that", Benjamin 1964
38. M. Takesaki, Conditional expectation in von Neumann algebra, J. Funct. Analysis 9, 306-321 (1972)
39. A. Thomae, "Ueber die höheren hypergeometrischen Reihen, ..." Math. Ann. 2, 427-444 (1870)
40. 1 and monodromy representations of braid group, Adv. Studies in Pure Math. 16, 297-372 (1988)
41. E. Verlinde, Fusion rules and modular transformations in 2D conformal field theory, Nuclear Phys. B 300, 360-376 (1988)
42. A. Wassermann, Operator algèbras and conformal field theory, Proc. I.C.M. Zurich (1994), 966-979, Birkhäuser
43. A. Wassermann, with contributions by V. Jones, "Lectures on operator algebras and conformal field theory", Proceedings of Borel Seminar, Bern 1994, to appear
44. A. Wassermann, Operator algebras and conformal field theory II: Fusion for von Neumann algebras and loop groups, to appear
45. A. Wassermann, Operator algebras and conformal field theory IV: Loop groups, quantum invariant theory and subfactors, in preparation
46. n and subfactors, Invent, math. 92, 249-383 (1988)
47. H. Weyl, "The classical groups", Princeton University Press 1946
48. E. Whittaker and G. Watson, "A course of modern analysis", 4th edition, C.U.P. 1927.
49. V. Jones, Fusion en algèbres de von Neumann et groupes de lacets (d'après A. Wassermann), Séminaire Bourbaki 1994-95, No. 800