The {$E\sb 7$} commuting squares produce {$D\sb {10}$} as principal graph
David E. Evans and Yasuyuki Kawahigashi
Source: Publ. Res. Inst. Math. Sci. Volume 30, Number 1 (1994), 151-166.
Primary Subjects: 46L37
Full-text: Open access
Links and Identifiers
Permanent link to this document: http://projecteuclid.org/euclid.prims/1195166280
Mathematical Reviews number (MathSciNet):
MR1266388
Zentralblatt MATH identifier:
0814.46054
Digital Object Identifier: doi:10.2977/prims/1195166280
References
[ABF] Andrews, G. E., Baxter, R. J. and Forrester, P. J., Eight vertex SOS model and generalized Rogers-Ramanujan type identities, J. Stat. Phys., 35 (1984), 193-266.
Mathematical Reviews (MathSciNet):
MR748075
Zentralblatt MATH:
0589.60093
[Ba] Baxter, R. J., Exactly solved models in statistical mechanics, Academic Press, New York, 1982.
Mathematical Reviews (MathSciNet):
MR690578
Zentralblatt MATH:
0723.60120
[BN] Bion-Nadal, J., An example of a subfactor of the hyperfinite II1 factor whose principal graph invariant is the Coxeter graph E6, in Current Topics in Operator Algebras, World Scientific Publishing, (1991), 104-113.
Mathematical Reviews (MathSciNet):
MR1193933
Zentralblatt MATH:
0816.46063
[BG] de Boer, J. and Goeree, J., Markov traces and II1 factors in conformal field theory, Comm. Math. Phys., 139 (1991), 267-304.
Mathematical Reviews (MathSciNet):
MR1120140
Zentralblatt MATH:
0760.57002
[CIZ] Cappelli, A., Itzykson, C. and Zuber, J.-B., The A-D-E classification of minimal and A11 conformal invariant theories, Comm. Math. Phys., 113 (1987), 1-26.
Mathematical Reviews (MathSciNet):
MR918402
Zentralblatt MATH:
0639.17008
[DJMO] Date, E., Jimbo, M., Miwa, T. and Okado, M., Solvable lattice models, in Theta functions-Bowdoin 1987, Part 1, Proc. Sympos. Pure Math. 49, Amer. Math. Soc., Providence, R.I., pp. 295-332.
Mathematical Reviews (MathSciNet):
MR1013138
Zentralblatt MATH:
0681.17014
[DJN] Durhuus, B., Jakobsen, H. P. and Nest, R., Topological quantum field theories from generalized 6j-symbols, preprint.
Mathematical Reviews (MathSciNet):
MR1219529
Zentralblatt MATH:
0808.57010
[DZ1] Di Francesco, P. and Zuber, J.-B., SU(N) lattice integrable models associated with graphs, Nucl. Phys., B338 (1990), 602-646.
Mathematical Reviews (MathSciNet):
MR1063590
[DZ2] Di Francesco, P. and Zuber, SU(N) lattice integrable models and modular invariance, to appear in Proc. Trieste Conf. Recent Developments in Conformal Field Theories, Trieste, 1989.
Zentralblatt MATH:
0748.17029
[DV] Dijkgraaf, R. and Verlinde, E., Modular invariance and the fusion algebra, Proceedings of the Annecy Conference on Conformal Field Theory, Nucl. Phys. B, Proc. Suppl., 5B (1988), 87-97.
Mathematical Reviews (MathSciNet):
MR1002959
Zentralblatt MATH:
0958.81510
[DHVM] Dixon, L., Harvey, J. A., Vafa, C. and Witten, E. Strings on orbifolds, Nucl. Phys., B261 (1985), 678-686, B274 (1986), 285-314.
Mathematical Reviews (MathSciNet):
MR818423
[E1] Evans, D. E., The C*-algebras of topological Markov chains, Tokyo Metropolitan University Lecture Notes, 1984.
[E2] Evans, D. E., Quasi-product states on C*-algebras, in Operator algebras and their connections with topology and ergodic theory, Springer Lect. Notes in Math., 1132 (1985), 129-151.
Mathematical Reviews (MathSciNet):
MR799567
Zentralblatt MATH:
0612.46057
[EG1] Evans, D. E. and Gould, J. D., Dimension groups and embeddings of graph algebras, to appear in Internal. J. Math.
Mathematical Reviews (MathSciNet):
MR1274121
Zentralblatt MATH:
0804.46067
[EG2] Evans, D. E. and Gould, Presentations of AF algebras associated to T-graphs, to appear in Publ. RIMS, Kyoto Univ.
[EK1] Evans, D. E. and Kawahigashi, Y., Orbifold subfactors from Hecke algebras, to appear in Comm. Math. Phys.
Mathematical Reviews (MathSciNet):
MR1301620
Zentralblatt MATH:
0805.46077
[EK2] Evans, D. E. and Kawahigashi, From subfactors to 3-dimensional topological quantum field theories and back, to appear in Asterisque.
Zentralblatt MATH:
0844.57014
[F] Fendley, P., New exactly solvable orbifold models, J. Phys., A22 (1989), 4633-4642.
Mathematical Reviews (MathSciNet):
MR1022137
Zentralblatt MATH:
0732.22018
[FG] Fendley, P. and Ginsparg, P., Non-critical orbifolds, Nucl. Phys., B324 (1989), 549-580.
[GHJ] Goodman, F., de la Harpe, P. and Jones, V. F. R., Coxeter graphs and towers of algebras, MSRI publications 14, Springer, 1989.
Mathematical Reviews (MathSciNet):
MR999799
Zentralblatt MATH:
0698.46050
[I1] Izumi, M., Application of fusion rules to classification of subfactors, Publ. RIMS, Kyoto Univ., 27 (1991), 953-994.
Mathematical Reviews (MathSciNet):
MR1145672
Zentralblatt MATH:
0765.46048
[I2] Izumi, M., On flatness of the Coxeter graph Es, to appear in Pac. J. Math.
Zentralblatt MATH:
0822.46073
[IK] Izumi, M. and Kawahigashi, Y., Classification of subfactors with the principal graph D( n 1}, J. Funct. Anal., 112 (1993), 257-286.
Mathematical Reviews (MathSciNet):
MR1213139
Zentralblatt MATH:
0791.46039
[Ji] Jimbo, M.(editor), Yang-Baxter equation in integrable systems, Adv. Ser. Math. Phys. 10, World Scientific, 1989.
Mathematical Reviews (MathSciNet):
MR1061379
Zentralblatt MATH:
0726.58005
[Jo] Jones, V. F. R., Index for subfactors, Invent. Math., 72 (1983), 1-15.
Mathematical Reviews (MathSciNet):
MR696688
Zentralblatt MATH:
0508.46040
[Kt] Kato, A., Classification of modular invariant partition functions in two dimensions, Mod. Phys. Lett., A2 (1987), 585-600.
Mathematical Reviews (MathSciNet):
MR906000
[Ka1] Kawahigashi, Y., On flatness of Ocneanu's connections on the Dynkin diagrams and classification of subfactors, to appear in J. Funct. Anal.
Mathematical Reviews (MathSciNet):
MR1308617
Zentralblatt MATH:
0829.46048
[Ka2] Kawahigashi, Y., Exactly solvable orbifold models and subfactors, in Functional Analysis and Related Topics, Led. Notes in Math. 1540, Springer Verlag, 1992.
Mathematical Reviews (MathSciNet):
MR1225815
Zentralblatt MATH:
0802.46074
[Ko] Rostov I., Free field presentation of the An coset models on the torus, Nucl. Phys., B300 (1988), 559-587.
Mathematical Reviews (MathSciNet):
MR965912
[O1] Ocneanu, A., Quantized group string algebras and Galois theory for algebras, in Operator algebras and applications, 2, Warwick, 1987, London Math. Soc. Lect. Note Series 136, Cambridge University Press, (1988) 119-172.
Mathematical Reviews (MathSciNet):
MR996454
Zentralblatt MATH:
0696.46048
[O2] Ocneanu, A., Graph geometry, quantized groups and nonamenable subfactors, Lake Tahoe Lectures, June-July, 1989.
[O3] Ocneanu, A., Quantum symmetry, differential geometry of finite graphs and classification of subfactors, University of Tokyo Seminary Notes 45, Notes recorded by Y. Kawahigashi, 1991.
[O4] Ocneanu, A., An invariant coupling between 3-manifolds and subfactors, with connections to topological and conformal quantum field theory, unpublished announcement, 1991.
[Ok] Okamoto, S., Invariants for subfactors arising from Coxeter graphs, in Current Topics in Operator Algebras, World Scientific Publishing, (1991), 84-103.
Mathematical Reviews (MathSciNet):
MR1193932
Zentralblatt MATH:
0809.46072
[Pa] Pasquier, V., Two-dimensional critical systems labelled by Dynkin diagrams, Nucl. Phys., B285 (1987), 162-172.
Mathematical Reviews (MathSciNet):
MR891835
[PP] Pimsner, M. and Popa, S., Entropy and index for subfactors, Ann. Scient. Ec. Norm Sup., 19 (1986), 57-106.
Mathematical Reviews (MathSciNet):
MR860811
Zentralblatt MATH:
0646.46057
[P1] Popa, S., Orthogonal pairs of *-subalgebras in finite von Neumann algebras, J. Operator Theory, 9 (1983), 253-268.
Mathematical Reviews (MathSciNet):
MR703810
Zentralblatt MATH:
0521.46048
[P2] Popa, S., Classification of subfactors: reduction to commuting squares, Invent. Math., 101 (1990), 19-43.
Mathematical Reviews (MathSciNet):
MR1055708
Zentralblatt MATH:
0757.46054
[P3] Popa, S., Classification of amenable subfactors of type II, to appear in Acta Math.
Mathematical Reviews (MathSciNet):
MR1278111
Zentralblatt MATH:
0853.46059
[R] Roche, Ph., Ocneanu cell calculus and integrable lattice models, Comm. Math. Phys., 127 (1990), 395-424.
Mathematical Reviews (MathSciNet):
MR1037111
Zentralblatt MATH:
0709.60536
[Sc] Schou, J., Commuting squares and indexfor subfactors, Ph. D. Thesis, Odense University, 1990.
[So] Sochen, N., Integrable models through representations of the Hecke algebra, Nucl. Phys., B360 (1991), 613-640.
Mathematical Reviews (MathSciNet):
MR1118801
[Su] Sunder, V. S., A model for AF-algebras and a representation of the Jones projections, J. Operator Theory, 18 (1987), 289-301.
Mathematical Reviews (MathSciNet):
MR915511
Zentralblatt MATH:
0693.46054
[SV] Sunder, V. S. and Vijayarajan, A. K., On the non-occurrence of the Coxeter graphs /?2M+i> E7, D2n + 1 as principal graphs of an inclusion of II1 factors, to appear in Pac. J. Math.
Zentralblatt MATH:
0798.43005
[TV] Turaev, V. G. and Viro, O. Y., State sum invariants of 3-manifolds and quantum 6j-symbols, Topology, 31 (1992), 865-902.
Mathematical Reviews (MathSciNet):
MR1191386
Zentralblatt MATH:
0779.57009
[W] Witten, E., Gauge theories and integrable lattice models, Nucl. Phys., B322 (1989), 629-697
Mathematical Reviews (MathSciNet):
MR1010205
[Z] Zuber, J.-B., Graphs, algebras, conformal field theories and integrable lattice models, Nucl. Phys. B(Proc. Suppl.), 18B (1990), 313-326.
Mathematical Reviews (MathSciNet):
MR1128151
Zentralblatt MATH:
0957.81667
Publications of the Research Institute for Mathematical Sciences