@article{RCP25_1997__48__1_0,
author = {Bauer, M. and Coste, A. and Itzykson, C. and Ruelle, P.},
title = {Comments on the {Links} {Between} $su(3)$ {Modular} {Invariants,} {Simple} {Factors} in the {Jacobian} of {Fermat} {Curves,} and {Rational} {Triangular} {Billiards}},
journal = {Les rencontres physiciens-math\'ematiciens de Strasbourg -RCP25},
note = {talk:1},
pages = {1--56},
year = {1997},
publisher = {Institut de Recherche Math\'ematique Avanc\'ee - Universit\'e Louis Pasteur},
volume = {48},
language = {en},
url = {https://www.numdam.org/item/RCP25_1997__48__1_0/}
}
TY - JOUR AU - Bauer, M. AU - Coste, A. AU - Itzykson, C. AU - Ruelle, P. TI - Comments on the Links Between $su(3)$ Modular Invariants, Simple Factors in the Jacobian of Fermat Curves, and Rational Triangular Billiards JO - Les rencontres physiciens-mathématiciens de Strasbourg -RCP25 N1 - talk:1 PY - 1997 SP - 1 EP - 56 VL - 48 PB - Institut de Recherche Mathématique Avancée - Université Louis Pasteur UR - https://www.numdam.org/item/RCP25_1997__48__1_0/ LA - en ID - RCP25_1997__48__1_0 ER -
%0 Journal Article %A Bauer, M. %A Coste, A. %A Itzykson, C. %A Ruelle, P. %T Comments on the Links Between $su(3)$ Modular Invariants, Simple Factors in the Jacobian of Fermat Curves, and Rational Triangular Billiards %J Les rencontres physiciens-mathématiciens de Strasbourg -RCP25 %Z talk:1 %D 1997 %P 1-56 %V 48 %I Institut de Recherche Mathématique Avancée - Université Louis Pasteur %U https://www.numdam.org/item/RCP25_1997__48__1_0/ %G en %F RCP25_1997__48__1_0
Bauer, M.; Coste, A.; Itzykson, C.; Ruelle, P. Comments on the Links Between $su(3)$ Modular Invariants, Simple Factors in the Jacobian of Fermat Curves, and Rational Triangular Billiards. Les rencontres physiciens-mathématiciens de Strasbourg -RCP25, Conférences de M. Bauer, A. Beauville, O. Babelon, A. Bilal, R. Stora, Tome 48 (1997), Exposé no. 1, 56 p.. https://www.numdam.org/item/RCP25_1997__48__1_0/
[1] , and , The A-D-E classification of minimal and conformal invariant theories, Commun. Math. Phys. 113 (1987) 1-26. | Zbl | MR
, Classification of modular invariant partition functions in two dimensions, Mod. Phys. Lett. A2 (1987) 585-600. | MR
[2] , The Classification of affine su(3) modular invariant partition functions, Commun. Math. Phys. 161 (1994) 233-264. | Zbl | MR
[3] , WZW commutants, lattices, and level-one partition functions, Nucl. Phys. B396 (1993) 708-736. | MR
[4] , and , Implications of an arithmetical symmetry of the commutant for modular invariants, Nucl. Phys. B402 (1993) 693-708. | Zbl | MR
[5] and , Remarks on Galois symmetry in rational conformal field theories, Phys. Lett. B323 (1994) 316-321. | MR
[6] and , Simple factors in the Jacobian of a Fermat curve, Can. J. Math. XXX (1978) 1183-1205. | Zbl | MR
[7] and , Rational billiards and algebraic curves, J. Geom. and Phys. 5 (1988) 191-208. | Zbl | MR
[8] Contributions by , , and in The Grothendieck theory of dessins d'enfants, L. Schneps ed., LMSLNS 200, Cambridge Univ. Press.
[9] , Infinite dimensional Lie algebras, 3rd edition, Cambridge University Press, Cambridge 1990. | Zbl | MR
[10] and , Théorie statistique des champs, editions du CNRS, Paris 1989.
[11] and , Modular and conformal invariance constraints in representation theory of affine algebras, Adv. Math. 70 (1988) 156-236. | Zbl | MR
[12] , Non-Abelian bosonization in two dimensions, Commun. Math. Phys. 92 (1984) 455-472. | Zbl
[13] and , Kac-Moody and Virasoro algebras in relation to quantum physics, Int. J. Mod. Phys. A1 (1983) 303-414. | Zbl | MR
[14] and , Naturality in conformal field theory, Nucl. Phys. B313 (1989) 16-40. | MR
[15] , The operator content of two-dimensional conformally invariant theories, Nucl. Phys. B270 (1986) 186-204. | Zbl | MR
[16] , Lie group exponents and SU(2) current algebras, Commun. Math. Phys. 118 (1988) 171-176. | Zbl | MR
[17] and , SU(N) lattice integrable models associated with graphs, Nucl. Phys. B338 (1990) 602-646. | MR
[18] , The level two and three modular invariants of SU(n), preprint (November 1995). | Zbl | MR
[19] , Towards a classification of modular invariant partition functions, J. Math. Phys. 36 (1995) 675-706. | Zbl | MR
[20] , and , Automorphism modular invariants of current algebras, Commun. Math. Phys. 179 (1996) 121-156. | Zbl | MR
[21] , Kac-Peterson, Perron-Frobenius, and the classification of conformal field theories, preprint (q-alg 9510026).
[22] and , Modular transformations of SU(N) affine characters and their commutant, Commun. Math. Phys. 127 (1990) 617-636. | Zbl | MR
[23] , Dimension of the commutant for the SU(N) affine algebras, Commun.Math. Phys. 133 (1990) 181-196. | Zbl | MR
[24] , , , and , Precise study of some number fields and Galois actions occurring in conformal field theory, Ann. Inst. Poincaré, Theor. Phys. 63 (1995) 41-79. | Zbl | MR | Numdam | EuDML
[25] , Toward classification of conformal theories, Phys. Lett. 206B (1988) 421-426. | MR
and , Rationality in conformal field theory, Commun. Math. Phys. 117 (1988) 441-450. | Zbl | MR
[26] and , Markov traces and II1 factors in conformal field theory, Commun. Math. Phys. 139 (1991) 267-304. | Zbl | MR
[27] , and , Modular invariants for affine theories at prime heights, Commun. Math. Phys. 133 (1990) 305-322. | Zbl | MR
[28] , , and , Modular invariants and fusion rule automorphisms from Galois theory, Phys. Lett. B334 (1994) 113-120. | MR
[29] , and , Galois modular invariants of WZW models, Nucl. Phys. B437 (1995) 667-694. | Zbl | MR
30] , Les Houches lectures "Introduction to compact Riemann surfaces, Jacobians and Abelian varieties", in From Number Theory to Physics, edited by M. Waldschmidt, P. Moussa, J.-M. Luck and C. Itzykson, Springer 1990. | Zbl | MR
[31] , Analytic theory of Abelian varieties, Cambridge University Press, Cambridge 1974. | Zbl | MR
[32] , Introduction to algebraic and Abelian functions, GTM 89, Springer 1982. | Zbl | MR
[33] , Simple factors of the Jacobian of a Fermat curve and the Picard number of a product of Fermat curves, Amer. J. Math. 113 (1991) 779-833. | Zbl | MR
[34] , appendix to , On the periods of Abelian integrals and a formula of Chowla and Seiberg, Invent. Math. 45 (1978) 193-211. | Zbl | MR | EuDML
[35] , Sur les périodes d'intégrales abéliennes, Commun. Pure and Appl. Math. XXIX (1976) 813-819. | Zbl | MR
[36] , Complex multiplication, Springer 1983. | Zbl | MR
[37] and , Complex multiplication of Abelian varieties and its applications to number theory, Publ. Math. Soc. Jap., no. 6, 1961. | Zbl | MR
[38] , Gamma function identities and elliptic differentials on Fermat curves, Duke Math. J. 45 (1978) 87-99. | Zbl | MR
[39] , Esquisse d'un programme. | Zbl
[40] , Elliptic curves, Princeton Univ. Press, Princeton 1992. | Zbl | MR
[41] Arithmetic and Geometry of Fermat Curves Proceedings of the Algebraic Geometry Seminar, Singapore (1987).
[42] and , Pseudo-integrable systems in classical and quantum mechanics, Physica 2D (1981) 495-512. | Zbl | MR
[43] , , String theory on group manifolds, Nucl. Phys. B278 (1986) 493-549. | MR
[44] , Lectures on modular forms Annals of Mathematics Studies 48, Princeton Univ. Press, Princeton 1992. | Zbl | MR
[45] and , Complex functions, Cambridge University Press, Cambridge 1987. | Zbl | MR
[46] , Tropics in complex function theory, Vol. II, Wiley & Sons 1971. | Zbl | MR
[47] , unpublished.
[48] , Polynomial invariants of finite groups, LMSLNS 190, Cambridge Univ. Press, Cambridge 1993. | Zbl | MR
[49] and , Finite unitary reflection groups, Can. J. Math. VI (1954) 274-304. | Zbl | MR






