@article{AIHPA_1995__63_1_41_0, author = {Buffenoir, E. and Coste, A. and Lascoux, J. and Degiovanni, P. and Buhot, A.}, title = {Precise study of some number fields and Galois actions occurring in conformal field theory}, journal = {Annales de l'I.H.P. Physique th\'eorique}, volume = {63}, year = {1995}, pages = {41-79}, mrnumber = {1354439}, zbl = {0868.12002}, language = {en}, url = {http://dml.mathdoc.fr/item/AIHPA_1995__63_1_41_0} }
Buffenoir, E.; Coste, A.; Lascoux, J.; Degiovanni, P.; Buhot, A. Precise study of some number fields and Galois actions occurring in conformal field theory. Annales de l'I.H.P. Physique théorique, Tome 63 (1995) pp. 41-79. http://gdmltest.u-ga.fr/item/AIHPA_1995__63_1_41_0/
[1] Operator content of 2d conformal field theories, Nucl. Phys., Vol. B. 270, 1986, pp. 186-204. | MR 845940 | Zbl 0689.17016
,[2] The ADE classification of A(1)1 and minimal conformal field theories, Comm. Math. Phys., Vol. 113, 1987, pp. 1-26. | MR 918402 | Zbl 0639.17008
, and ,Théorie Statistique des Champs, CNRS, Paris, 1989.
and ,Thèse, unpublished.
,[3] Remarks on Galois symmetry in RCFT, Phys. Lett., Vol. B 323, 1994, pp. 316-321. | MR 1266785
and ,[4] Markov traces and type II1 factors in conformal field theory, Comm. Math. Phys., Vol. 139, 1991, p. 267. | MR 1120140 | Zbl 0760.57002
and ,[5] Moore and Seiberg equations, topological field theories and Galois theory, in The Grothendieck theory of dessins d'enfants, L. SCHNEPS Ed., London Mathematical Society, Lecture Note Series, Vol. 200, 1993, pp. 359-368. | MR 1305404 | Zbl 0822.57024
,[6] Polynomial equations for rational conformal field theories, Phys. Lett. B., Vol. 212, 1988, pp. 451-460. | MR 962600
and ,[7] Classical and quantum conformal field theory, Comm. Math. Phys., Vol. 123, 1989, pp. 177-255. | MR 1002038 | Zbl 0694.53074
and ,[8] Modular invariance and the fusion algebra, Conformal Field Theories and Related Topics, P. BINÉTRUY, P. SORBA and R. STORA Eds., Nucl. Phys. B. (Proc. Suppl.), Vol. 5, North Holland, 1988, pp. 87-97. | MR 1002959 | Zbl 0958.81510
, and ,[9] Classification of modular invariant partition functions in two dimensions, Mod. Phys. Lett., Vol. A2, 1987, pp. 585-600. | MR 906000
,[10] 396, 1993, pp. 708; and The classification of affine su(3) modular invariant partition functions, Comm. Math. Phys. Vol. 161, 1994, pp. 233-264. | MR 1218796 | Zbl 0806.17031
, Nucl. Phys. Vol. BThe classification of Affine SU(3) Modular Invariant Partition Functions Revisited, texfile hep-th-9404185. T. GANNON and Q. HO-KIM, The low level modular invariant partition functions of rank two algebras, Int. J. Mod. Phys., Vol. A 9, 1994, pp. 2667-2686. | MR 1277039 | Zbl 0985.81532
,The rank four heterotic modular invariant partition functions, Nucl. Phys., Vol. B 425, 1994, pp. 319-342 | MR 1292630 | Zbl 1049.81625
and ,[11] Implications of an arithmetical symmetry of the commutant for modular invariants, Nucl. Phys., Vol. B 402, 1993, pp. 693-708. | MR 1236194 | Zbl 1043.81698
, and ,Thesis, unpublished.
,[12] Quantum field theory and the Jones polynomial, Comm. Math. Phys., Vol. 121, 1989, pp. 351-399. | Zbl 0667.57005
,[13] Invariants of 3-manifolds via link polynomials and quantum groups, Invent. Math., Vol. 103, 1991, pp. 547-597. | MR 1091619 | Zbl 0725.57007
and ,[14] Quasi-quantum groups, three manifolds and topological field theory, Comm. Math. Phys. Vol. 150, 1992, pp. 83-107. | MR 1188498 | Zbl 0773.57004
and ,[15] Moore and Seiberg's equations and 3D topological field theories, Comm. Math. Phys., Vol. 145, 1992, pp. 459-505. | MR 1162357 | Zbl 0753.57010
,[16] Topological invariants for 3-manifolds using representations of mapping class groups (1), Topology, Vol. 31, 1992, pp. 203-230. | MR 1167165 | Zbl 0762.57011
,[17] Equations de Moore et Seiberg, théories topologiques et théorie de Galois, Preprint ENSLAPP-L-458-94, March 1994. | MR 1325107
,[18] Esquisse d'un programme, Rapport Scientifique, 1984, unpublished,
,[19] Z/NZ Conformal Field Theories, Comm. Math. Phys., Vol. 127, 1990, pp. 71-99. | MR 1036115 | Zbl 0696.17012
,[20] Abrégé d' histoire des mathématiques, sous la direction de , Hermann, Paris, 1986. | MR 864980
Algèbre commutative, Masson, 1985. | MR 790684 | Zbl 0584.13001
,[21] Fusion potentials (1), J. Phys., Vol. A 26, 1993, pp. 1441-1454. | MR 1212013 | Zbl 0778.17021
and ,[22] On the structure of fusion algebras, Phys. Lett., Vol. B 217, 1989, pp. 247-251. | MR 980656
,[23] String theory on group manifolds, Nucl. Phys., Vol. B 278, 1986, pp. 493-549. | MR 862896
and ,[24] Modular invariants and fusion rule automorphisms from Galois theory, Phys. Lett., Vol. B 334, 1994, pp. 113-120. | MR 1290075
, , , and ,[25] Fusion rings and geometry, Comm. Math. Phys., Vol. 141, 1991, pp. 381-411. | MR 1133272 | Zbl 0752.17033
,Fusion Potentials for Gk and handle squashing, Nucl. Phys., Vol. B 393, 1993, p. 361. | MR 1214324
,[26] Introduction to Lie algebras and their representations, Springer GTM. | Zbl 0254.17004
,[27] Ideals, Varieties and Algorithms, Springer U.T.M., 1991.
, and ,A Course in Computational Algebraic Number Theory, Springer G.T.M. 138, 1993. | MR 1228206 | Zbl 0786.11071
,[28] Introduction to Number Theory, Springer (82). | MR 665428 | Zbl 0483.10001
,Vorlesungen über die Theorie der algebraischen Zahlen, Chapter 3, reprinted in german by Chelsea. | JFM 49.0106.10 | Zbl 0041.01102
,[29] Springer proc. in Phys., J. M. LUCK, P. MOUSSA and M. WALDSCHMIDT Eds., Vol. 47, 1990, pp. 20-32, | Zbl 0716.17030
and ,[30] On Knots, Princeton Univ. Press.
, proc. J. Hopkins workshop, Florence, 1989, LUSANNA et al. Eds., World Scientific,[31] A calculus for framed links in S3, Invent. Math., Vol. 45, 1978, pp. 35-56. | MR 467753 | Zbl 0377.55001
,[32] The topology of 4-manifolds, Lecture Notes in Mathematics, Vol. 1374, Springer Verlag, 1989. | MR 1001966 | Zbl 0668.57001
,[33] On the 3-manifold invariants of Witten and Reshetikhin-Turaev for sl(2, C), 1991, | MR 1117149
and ,[34] Invariants of 3-manifolds based on Conformal Field Theory and Heegard splittings, Quantum groups, (P. P. KULISH ed., Lecture notes in Mathematics, Vol. 1510, Springer-Verlag, 1990, pp. 341-349. | MR 1183499 | Zbl 0752.57008
,[35] Algebraic number theory, Addison-Wesley (Reading), 1970. | MR 282947 | Zbl 0211.38404
,[36] Invariants of three-manifolds from the combinatorics of the Jones polynomial, Carribridge University, Preprint, 1991. | MR 1105702
,[37] Cours d'arithméthique, P.U.F., 1970. | Zbl 0225.12002
,