Chiral structure of modular invariants for subfactors

Communications in Mathematical Physics

Volumn 210, Issue 3, 2000, Pages 733-784

  Böckenhauer, Jens ^a   Evans, David E ^a   Kawahigashi, Yasuyuki ^b  

^a CARDIFF UNIVERSITY   (United Kingdom)

^b UNIVERSITY OF TOKYO   (Japan)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0034349894     PISSN: 00103616     EISSN: None     Source Type: Journal    
DOI: 10.1007/s002200050798     Document Type: Article

References (42)

1. 1. Böckenhauer, J.. Evans, D.E.: Modular invariants, graphs and α-induction for nets of subfactors. I. Commun. Math. Phys. 197, 361-386 (1998)
2. 2. Böckenhauer, J., Evans, D.E.: Modular invariants, graphs and α-induction for nets of subfactors. II. Commun. Math. Phys. 200, 57-103 (1999)
3. 3. Böckenhauer, J., Evans, D.E.: Modular invariants, graphs and α-induction for nets of subfactors. III. Commun. Math. Phys. 205, 183-228 (1999)
4. 4. Böckenhauer, J., Evans, D.E., Kawahigashi, Y.: On α-induction, chiral generators and modular invariants for subfactors. Commun. Math. Phys. 208, 429-487 (1999)
5. 5. Cappelli, A., Itzykson, C., Zuber, J.-B.: Modular invariant partition functions in two dimensions. Nucl. Phys. B 280, 445-465 (1987)
6. 1 conformal invariant theories. Commun. Math. Phys. 113. 1-26 (1987)
7. 7. Di Francesco, P., Zuber, J.-B.: SU (N) lattice integrable models associated with graphs. Nucl. Phys. B 338, 602-646 (1990)
8. 8. Di Francesco, P., Zuber, J.-B.: SU (N) lattice integrable models and modular invariance In: S. Randjbar et al (eds.), Recent Developments in Conformal Field Theories, Singapore: World Scientific, 1990, pp. 179-215
9. 9. Doplicher, S., Haag, R., Roberts, J.E.: Fields, observables and gauge transformations. I. Commun. Math. Phys. 13, 1-23 (1969)
10. 10. Evans, D.E., Kawahigashi, Y.: Quantum symmetries on operator algebras. Oxford: Oxford University Press, 1998
11. 11. Fredenhagen, K., Rehren, K.-H., Schroer, B.: Superselection sectors with braid group statistics and exchange algebras. II. Rev. Math. Phys. Special issue 113-157 (1992)
12. 12. Fröhlich, J., Gabbiani, F.: Braid statistics in local quantum theory. Rev. Math. Phys. 2, 251-353 (1990)
13. 13. Gannon, T.: WZW commutants, lattices and level-one partition functions. Nucl. Phys. B 396, 708-736 (1993)
14. 14. Gannon, T.: The classification of affine SU (3) modular invariants. Commun. Math. Phys. 161, 233-264 (1994)
15. 15. Gato-Rivera, B., Schellekens, A.N.: Complete classification of simple current automorphisms. Nucl. Phys. B 353, 519-537 (1991)
16. 16. Goodman, F., de la Harpe, P., Jones, V.F.R.: Coxeter graphs and towers of algebras. MSRI publications 14, Berlin: Springer, 1989
17. 17. Guido, D., Longo, R.: The conformal spin and statistics theorem. Commun. Math. Phys. 181, 11-35 (1996)
18. 18. Itzykson, C.: From the harmonic oscillator to the A-D-E classification of conformal models. Adv. Stud. in Pure Math. 19, 287-346 (1989)
19. 19. Izumi, M.: Application of fusion rules to classification of subfactors. Publ. RIMS, Kyoto Univ. 27, 953-994 (1991)
20. 20. Jones, V.F.R.: Index for subfactors. Invent. Math. 72, 1-25 (1983)
21. 21. Kac, V.G.: Infinite dimensional Lie algebras. 3rd edition, Cambridge: Cambridge University Press, 1990
22. 22. Kato, A.: Classification of modular invariant partition functions in two dimensions. Modern Phys. Lett. A 2, 585-600 (1987)
23. 23. Kawai, T.: On the structure of fusion rule algebras. Phys. Lett. B 217, 247-251 (1989)
24. 24. Kosaki, H.: Extension of Jones theory on index to arbitrary factors. J. Funct. Anal. 66, 123-140 (1986)
25. 25. Longo, R.: A Duality for Hopf algebras and for subfactors I. Commun. Math. Phys. 159, 133-150 (1994)
26. 26. Longo, R., Rehren, K.-H.: Nets of subfactors. Rev. Math. Phys. 7, 567-597 (1995)
27. 27. Moore, G., Seiberg, N.: Naturality in conformal field theory. Nucl. Phys. B 313, 16-40 (1989)
28. 28. Nahm, W.: Lie group exponents and SU (2) current algebras. Commun. Math. Phys. 118, 171-176 (1988)
29. 29. Ocneanu, A.: Quantum symmetry, differential geometry of finite graphs and classification of subfactors. Univ. of Tokyo Seminary Notes 45, 1991 (Notes recorded by Y. Kawahigashi)
30. 30. Ocneanu, A.: Paths on Coxeter diagrams: From Platonic solids and singularities to minimal models and subfactors. (Notes recorded by S. Goto). In: B.V. Rajarama Bhat et al. (eds.), Lectures on operator theory, The Fields Institute Monographs, Providence, RI: AMS publications 2000, pp. 243-323
31. 31. Okamoto, S.: Invariants for subfactors arising from Coxeter graphs. In: H. Araki et al. (eds.), Current Topics in Operator Algebras, Singapore: World Scientific 1991, pp. 84-103
32. 32. Pasquier, V.: Etiology of IRF models. Commun. Math. Phys. 118, 355-364 (1988)
33. 33. Petkova, V.B., Zuber, J.-B.: From CFT to graphs. Nucl. Phys. B 463, 161-193 (1996)
34. 34. Popa, S.: Classification of subfactors and of their endomorphisms. CBMS Regional Conference Series, Am. Math. Soc. 86, (1995)
35. 35. Rehren, K.-H.: Braid group statistics and their superselection rules. in: D. Kastler (ed.), The algebraic theory of superselection sectors, Palermo, 1989, Singapore: World Scientific, 1990, pp. 333-355
36. 36. Rehren, K.-H.: Space-time fields and exchange fields. Commun. Math. Phys. 132, 461-483 (1990)
37. 37. Rehren, K.-H.: Chiral observables and modular invariants. Commun. Math. Phys. 208, 689-712 (2000)
38. 38. Schellekens, A.N., Yankielowicz, S.: Extended chiral algebras and modular invariant partition functions. Nucl. Phys. B 327, 673-703 (1989)
39. 39. Wassermann, A.: Operator algebras and conformal field theory III: Fusion of positive energy representations of LSU (N) using bounded operators. Invent. Math. 133, 467-538 (1998)
40. n and subfactors. Invent. Math. 92, 345-383 (1988)
41. 41. Xu, F.: New braided endomorphisms from conformal inclusions. Commun. Math. Phys. 192, 347-403 (1998)
42. 42. Xu, F.: Applications of braided endomorphisms from conformal inclusions. Internat. Math. Research Notices, 1998, pp. 5-23, see also the erratum to Theorem 3.4 (1) on p. 437 of the same volume