Jones, Vaughan
Fusion en algèbres de von Neumann et groupes de lacets
Séminaire Bourbaki, Tome 37 (1994-1995) , Exposé no. 800 , p. 251-273
Zbl 0921.46066 | MR 1423627
URL stable : http://www.numdam.org/item?id=SB_1994-1995__37__251_0

Bibliographie

[Ar] H. Araki - Canonical anticommutation relations, Contemporary Math. 62 (1987), 23-186. MR 878376

[A] M. Atiyah - Topological quantum field theory, Publ. IHES 68 (1989), 175-186. Numdam | MR 1001453 | Zbl 0692.53053

[BSZ] J.C. Baez, I.E. Segal et Z. Zhou - Introduction to algebraic and constructive quantum field theory, Princeton University Press (1992). MR 1178936 | Zbl 0760.46061

[Ba] R. Baxter - Exactly solved models in statistical mechanics, Academic Press, New York, 1982. MR 690578 | Zbl 0723.60120

[BW] J. Birman et H. Wenzl - Braids, link polynomials and a new algebra, Trans. AMS 313 (1989), 269-273. MR 992598 | Zbl 0684.57004

[Bi] J. Birman - Braids, links and mapping class groups, Ann. Math. Studies 82 (1974). MR 375281 | Zbl 0305.57013

[Bo] R. Borcherds - Vertex algebras, Kac-Moody algebras and the Monster, Proc. Nat. Acad. Sci. U.S.A. 83 (1986), 3068-3071. MR 843307 | Zbl 0613.17012

[Br] R. Brauer - On algebras which are connected with the semisimple continuous groups, Ann. Math. 38 (1937), 856-872. Zbl 0017.39105

[Ca] P. Cartier - Développements récents sur les groupes de tresses. Applications à la topologie et à l'algèbre, Sém. Bourbaki, exp. 716, Astérisque 189-190 (1990), 17-67. Numdam | MR 1099871 | Zbl 0737.57001

[CIZ] A. Cappelli, C. Itzykson et J.B. Zuber, Nucl. Phys. B 280 (1987), 445- . MR 881119 | Zbl 0661.17017

[Co1] A. Connes - Noncommutative geometry, Academic Press, 1994. MR 1303779 | Zbl 0818.46076

[Co2] A. Connes - Classification of injective factors, Ann. Math. 104 (1976), 73- 115. MR 454659 | Zbl 0343.46042

[Co3] A. Connes - Une classification des facteurs de type III, Ann. Sci. Ec. Norm. Sup. 4e série 6 (1973), 133-252. Numdam | MR 341115 | Zbl 0274.46050

[DHR] S. Doplicher, R. Haag et J. Roberts - Local observables and particle statistics, I, II, Comm. Math. Phys. 23 (1971), 199-230 and 35 (1974), 49-85. MR 297259

[Dr] V. Drinfeld - Quantum groups, Proc. ICM 1986, vol. 1, 798-820. MR 934283

[Fa] L. Faddeev - Integrable models in (1 + 1)-dimensional quantum field theory, (Lectures in Les Houches, 1982) Elsevier Science Publishers, 1984, 563-608. MR 782509

[FR] R. Fenn et C. Rourke - On Kirby's calculus of links, Topology 18 (1979), 1-15. MR 528232 | Zbl 0413.57006

[FRS] K. Fredenhagen, Rehren, et B. Schroer - Superselection sectors with braid group statistics and exchange algebras, Comm. Math. Phys. 125 (1989), 201-226. MR 1016869 | Zbl 0682.46051

[F+] P. Freyd, D. Yetter, J. Hoste, W. Lickorish, K. Millett et A. Ocneanu - A new polynomial invariant of knots and links, Bull. AMS 12 (1985), 183-190. MR 776477 | Zbl 0572.57002

[FQS] D. Friedan, Z. Qiu et S. Shenker - Conformal invariance, unitarity and critical exponents in two dimensions, Phys. Rev. Lett. 52 (1984), 1575-1578. MR 740343

[Fr] J. Frölich - Statistics of fields, the Yang-Baxter equation and the theory of knots and links, Proceedings of Cargèse, ed. G. 't Hooft et al. (1987). MR 1008276

[GO] P. Goddard et D. Olive - Kac-Moody and Virasoro algebras, Adv. Series in Math. Phys. 3, World Scientific (1988). MR 966668 | Zbl 0661.17001

[GHJ] F. Goodman, P. De La Harpe et V. Jones - Coxeter graphs and towers of algebras, MSRI Publications (Springer) 14 (1989). MR 999799 | Zbl 0698.46050

[GW] F. Goodman et H. Wenzl - Littlewood Richardson coefficients for Hecke algebras at roots of unity, Adv. Math. 82 (1990), 244-265. MR 1063959 | Zbl 0714.20004

[HK] R. Haag et D. Kastler - An algebraic approach to quantum field theory, J. Math. Phys. 5 (1964), 848-861. MR 165864 | Zbl 0139.46003

[H] R. Haag - Local quantum physics, Springer-Verlag (1992). MR 1182152 | Zbl 0777.46037

[Ha] U. Haagerup - Connes' bicentralizer problem and the uniqueness of the injective factor of type III1, Acta Math. 158 (1987), 95-148. MR 880070 | Zbl 0628.46061

[Ji1] M. Jimbo - A q-difference analogue of U(g) and the Yang-Baxter equation, Lett. Math. Phys. 102 (1986), 537-567. MR 797001 | Zbl 0587.17004

[Ji2] M. Jimbo - it A q-analogue of U(sl(N + 1)), Hecke algebra and the Yang-Baxter equation, Lett. Math. Phys. 11 (1986), 247-252. MR 841713 | Zbl 0602.17005

[Jo1] V. Jones - Index for subfactors, Invent. Math. 72 (1983), 1-25. MR 696688 | Zbl 0508.46040

[Jo2] V. Jones - Notes on subfactors and statistical mechanics, in : Braid Groups, Knot Theory and Statistical Mechanics (ed. Yang & Ge), World Scientific, 1989, 1-25. MR 1062421 | Zbl 0725.46038

[Jo4] V. Jones - Braid groups, Hecke algebras and type II1 factors, in : Geometric Methods in Operator Algebras. (ed. Araki and Effros), Pitman Res. Notes in Math. (1983), 242-273. MR 866500 | Zbl 0659.46054

[Jo5] V. Jones - A polynomial invariant for knots via von Neumann algebras, Bull. AMS 12 (1985), 103-111. MR 766964 | Zbl 0564.57006

[JW] V. Jones and A. Wassermann - Fermions on the circle and representations of loop groups, à paraître.

[Kc] V. Kac - Infinite dimensional Lie algebras, 3ème édition, Cambridge University Press (1990). MR 1104219 | Zbl 0925.17021

[KL] V. Kazhdan and G. Lusztig - Tensor structures arising from affine Lie algebras, IV, Journal AMS 7 (1994), 383-453. MR 1239507 | Zbl 0802.17008

[KZ] V. Knizhnik et A. Zamolodchikov - Current algebra and Weiss-Zumi no models in two dimensions, Nucl. Phys. B 247 (1984), 83-103. MR 853258 | Zbl 0661.17020

[KR] P. Kulish et N. Reshetikhin - Quantum linear problem for the sine-Gordon equation and higher representations, J. Sov. Math. 23 (1983), 2435-2441.

[Li1] W. Lickorish - Polynomials for links, Bull. AMS 20 (1988), 558-588. MR 980759 | Zbl 0685.57001

[Lo] R. Longo - Index of subfactors and statistics of quantum fields, I, Comm. Math. Phys. 126 (1989), 217-247. MR 1027496 | Zbl 0682.46045

[LO] T. Loke - Operator algebras and conformal field theory of the discrete series representations of Diff(S1), Thèse, Université de Cambridge (1994).

[MSe] G. Moore et N. Seiberg - Classical and quantum conformal field theory, Comm. Math. Phys. 123 (1989), 177-254. MR 1002038 | Zbl 0694.53074

[MvN] F. Murray et J. Von Neumann - On rings of operators, Ann. Math. 37 (1936), 116-229. MR 1503275 | Zbl 0014.16101

[NT] T. Nakanishi and A. Tsuchiya - Level-rank duality of WZW models in conformal field theory, Comm. Math. Phys. 144 (1992), 351-372. MR 1152377 | Zbl 0751.17024

[O2] A. Ocneanu - Quantized groups, string algebras and Galois theory for algebras, in : Operator Algebras and Applications (eds. Evans and Takesaki), 1988, 119-172. MR 996454 | Zbl 0696.46048

[Pa] V. Pasquier - Two-dimensional critical systems labeled by Dynkin diagrams, Nucl. Phys. B 285 (1987), 162-172. MR 891835

[Po1] S. Popa - Classification of subfactors: the reduction to commuting squares. Invent. Math. 101 (1990), 19-43. MR 1055708 | Zbl 0757.46054

[Po2] S. Popa - Classification of subfactors and of their endormorphisms, à paraître dans Lecture Notes, CBMS series. Zbl 0865.46044

[PP] M. Pimsner et S. Popa - Entropy and index for subfactors, Ann. Sci. Ec. Norm. Sup. 19 (1986), 57-106. Numdam | MR 860811 | Zbl 0646.46057

[PS] A. Pressley et G. Segal - Loop Groups, Oxford Science Publications (1986). MR 900587 | Zbl 0618.22011

[PSt] R. Powers et E. Størmer - Free states of the canonical anticommutation relations, Comm. Math. Phys. 16 (1970), 1-33. MR 269230 | Zbl 0186.28301

[Sa] J.-L. Sauvageot - Sur le produit tensoriel relatif d'espaces de Hilbert, J. Operator Theory, 9 (1983), 237-252. MR 703809 | Zbl 0517.46050

[Se] G. Segal - Notes on conformal field theory, unpublished manuscript.

[Sk] E. Sklyanin - Some algebraic structures connected with the Yang-Baxter equation, J. Sov. Math. 19 (1982), 1546-1596. MR 684124 | Zbl 0497.35072

[Ta1] M. Takesaki - Tomita's theory of modular Hilbert algebras and its applications, Lecture Notes in Math., vol. 128, Springer, 1970. MR 270168 | Zbl 0193.42502

[Ta2] M. Takesaki - Conditional expectations in von Neumann algebras, Journal Funct. Analysis 9 (1972), 306-321. MR 303307 | Zbl 0245.46089

[TL] H. Temperley et E. Lieb - Relations between the 'percolation' and... , Proc. Roy. Soc. Ser. A 322 (1971), 251-280. MR 498284 | Zbl 0211.56703

[TK] A. Tsuchiya et Y. Kanie - Vertex operators in conformal field theory on P1 and monodromy representations of braid group, Adv. Stud. Pure Math. 16 (1988), 297-372. MR 972998 | Zbl 0661.17021

[TUY] A. Tsuchiya, K. Ueno et Y. Yamada - Conformal field theory on universal family of stable curves with gauge symmetries, Adv. Studies in Pure Maths. 19 (1989), 459-566. MR 1048605 | Zbl 0696.17010

[Tu] V. Turaev - The Yang-Baxter equation and invariants of links, Invent. Math. 92 (1988), 527-553. MR 939474 | Zbl 0648.57003

[V] E. Verlinde - Fusion rules and modular transformations in 2D conformal field theory, Nuclear Phys. B 300 (1988), 360-376. MR 954762 | Zbl 1180.81120

[Wa1] A. Wassermann - Coactions and Yang-Baxter equations for ergodic actions and subfactors, in : Operator Algebras and Applications (eds. Evans and Takesaki), 1988 (LMS Lecture Notes 136), 203-236. MR 996457 | Zbl 0809.46079

[Wa2] A. Wassermann - Fusion for von Neumann algebras and loop groups, à paraître.

[Wa3] A. Wassermann - Loop groups, invariant theory and subfactors, à paraître.

[Wa4] A. Wassermann - Operator algebras and conformal field theory, à paraître dans Proceedings du Congrès International (1994). MR 1403996 | Zbl 0854.46055

[We1] H. Wenzl - Hecke algebras of type An and subfactors, Invent. Math. 92 (1988), 349-383. MR 936086 | Zbl 0663.46055

[We2] H. Wenzl - Quantum groups and subfactors of type B, C and D, Comm. Math. Phys. 133 (1990), 383-432. MR 1090432 | Zbl 0744.17021

[We3] H. Wenzl - On the structure of Brauer's centralized algebras, Ann. Math. 128 (1988), 173-193. MR 951511 | Zbl 0656.20040

[Wi] E. Witten - Quantum field theory and the Jones polynomial, Comm. Math. Phys. 121 (1989), 351-399. MR 990772 | Zbl 0667.57005