The level 2 and 3 modular invariants for the orthogonal algebras

Canadian Journal of Mathematics

Volumn 52, Issue 3, 2000, Pages 503-521

  Gannon, Terry ^a  

^a UNIVERSITY OF ALBERTA   (Canada)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0034394485     PISSN: 0008414X     EISSN: None     Source Type: Journal    
DOI: 10.4153/CJM-2000-023-2     Document Type: Article

References (26)

1. M. Bauer, A. Coste, C. Itzykson and Ph. Ruelle, Comments on the links between SU(3) modular invariants, simple factors in the Jacobian of Fermat curves, and rational triangular billiards. J. Geom. Phys. 22(1997), 134-189;
2. Ph. Ruelle, E. Thiran and J. Weyers, Implications of an arithmetic symmetry of the commutant for modular invariants. Nucl. Phys. B402(1993), 693-708.
3. D. Bernard, String characters from Kac-Moody automorphisms. Nucl. Phys. B288(1987), 628-648.
4. 1 and minimal conformal field theories. Commun. Math. Phys. 113(1987), 1-26.
5. A. Coste and T. Cannon, Remarks on Galois symmetry in rational conformal field theories. Phys. Lett. B323(1994), 316-321.
6. D. E. Evans and Y. Kashahigashi, Quantum Symmetries on Operator Algebras. Oxford University Press, Oxford, 1998.
7. J. Fuchs, A. N. Schellekens and C. Schweigert, Galois modular invariants of WZW models. Nucl. Phys. B437(1995), 667-694.
8. T. Gannon, WZW commutants, lattices, and level-one partition functions. Nucl. Phys. B396(1993), 708-736.
9. _, Symmetries of the Kac-Peterson modular matrices of affine algebras. Invent. Math. 122(1995), 341-357.
10. _, The classification of SU(3) modular invariants revisited. Ann. Inst. H. Poincaré Phys. Théor. 65(1996), 15-56.
11. _, The level 2 and 3 modular invariant partition functions for SU(n). Lett. Math. Phys. 39(1997), 289-298.
12. m modular invariants, N = 2 minimal models, and the quantum Hall effect. Nucl. Phys. 491(1997), 659-688.
13. _, The Cappelli-Itzykson-Zuber A-D-E classification. Preprint math.QA/9902064; Rev. Math. Phys., to appear.
14. _, The Cappelli-Itzykson-Zuber A-D-E classification. Preprint math.QA/9902064; Rev. Math. Phys., to appear.
15. _, Kac-Peterson, Perron-Frobenius, and the classification of conformal field theories. Preprint q-alg/9510026;
16. 7-type invariants of affine algebras. In preparation.
17. T. Gannon, Ph. Ruelle and M.A. Walton, Automorphism modular invariants of current algebras. Commun. Math. Phys. 179(1996), 121-156.
18. A. Hanany and Y.-H. He, Non-abelian finite gauge theories. Preprint hep-th/9811183.
19. V. G. Kac and D. Peterson, Infinite-dimensional Lie algebras, theta functions and modular forms. Adv. Math. 53(1984), 125-264.
20. V. G. Kac and M. Wakimoto, Modular and conformal constraints in representation theory of affine algebras. Adv. Math. 70(1988), 156-236.
21. N. Koblitz and D. Rohrlich, Simple factors in the Jacobian of a Fermat curve. Canad. J. Math. 30(1978), 1183-1205.
22. E. J. Mlawer, S. G. Naculich, H. A. Riggs and H. J. Schnitzer, Group-level duality of WZW fusion coefficients and Chern-Simons link observables. Nucl. Phys. B352(1991), 863-896.
23. A. N. Schellekens, Cloning SO(N) level 2. Internat. J. Modern Phys. A14(1999), 1283-1291.
24. A. N. Schellekens and S. Yankielowicz, Modular invariants from simple currents. An explicit proof. Phys. Lett. B227(1989), 387-391.
25. P. Slodowy, Platonic solids, Kleinian singularities, and Lie groups. Lecture Notes in Math. 1008, Springer-Verlag, New York, 1983, 102-138.
26. D. Versiegen, New exceptional modular invariant partition functions for simple Kac-Moody algebras. Nucl. Phys. B346(1990), 349-386.