MacDonald, I. G.
Affine Lie algebras and modular forms
Séminaire Bourbaki, Tome 23 (1980-1981) , Exposé no. 577 , p. 258-276
Zbl 0472.17006 | MR 647501 | 1 citation dans Numdam
URL stable : http://www.numdam.org/item?id=SB_1980-1981__23__258_0

Bibliographie

[1] M. Adler and P. Van Moerbeke, Completely integrable systems, Kac-Moody Lie algebras and curves, Adv.in Math. 36(1980) 1-44.

[2] M. Adler and P. Van Moerbeke, Linearisation of Hamiltonian systems, Jacobi varieties and representation theory, Adv. in Math. 38(1980) 318-379. MR 597730 | Zbl 0455.58010

[3] J.H. Conway and S.P. Norton, Monstrous moonshine, Bull. LMS 11(1979) 308-339. MR 554399 | Zbl 0424.20010

[4] M. Demazure, Identités de Macdonald, Sém.Bourbaki 483 (1976). Numdam | Zbl 0345.17003

[5] A. Feingold and J. Lepowsky, The Weyl-Kac character formula and power series identities, Adv. in Math. 29(1978) 271-309. MR 509801 | Zbl 0391.17009

[6] I.B. Frenkel, Orbital theory for affine Lie algebras, Inv. Math. (to appear). MR 752823 | Zbl 0548.17007

[7] I.B. Frenkel and V.G. Kac, Basic representations of affine Lie algebras and dual resonance models, Inv. Math. 62(1980) 23-66. MR 595581 | Zbl 0493.17010

[8] H. Garland, Dedekind's n-function and the cohomology of infinite-dimensional Lie algebras, PNAS 72(1975) 2493-2495. MR 387361 | Zbl 0322.18010

[9] H. Garland, The arithmetic theory of loop groups, preprint. MR 601519

[10] H. Garland and J. Lepowsky, Lie algebra homology and the Macdonald-Kac formulas, Inv. Math. 34(1976) 37-76. MR 414645 | Zbl 0358.17015

[11] V.G. Kac, Simple irreducible graded Lie algebras of finite growth, Math. USSR Izvestiya 2(1968) 1271-1311. MR 259961 | Zbl 0222.17007

[12] V.G. Kac, Infinite-dimensional Lie algebras and Dedekind's n-function, Funct.Anal. Appl. 8(1974) 68-70. MR 374210 | Zbl 0299.17005

[13] V.G. Kac, Infinite-dimensional Lie algebras, Dedekind's n-function, classical Möbius formula and the very strange formula, Advances in Math. 30(1978) 85-136. MR 513845 | Zbl 0391.17010

[14] V.G. Kac, Infinite root systems, representations of graphs and invariant theory, Inv. Math. 56(1980) 57-92. MR 557581 | Zbl 0427.17001

[15] V.G. Kac, An elucidation of "Infinite-dimensional algebras ... and the very strange formula". E8(1) and the cube root of the modular invariant j. Advances in Math. 35(1980) 264-273. MR 563927 | Zbl 0431.17009

[16] V.G. Kac and D. Peterson, Affine Lie algebras and Hecke modular forms, Bull. AMS (New Series) 3(1980) 1057-1061. MR 585190 | Zbl 0457.17007

[17] V.G. Kac and D. Peterson, Infinite-dimensional Lie algebras, theta functions and modular forms, preprint. MR 750341

[18] V.G. Kac, D.A. Kazhdan, J. Lepowsky and R.L. Wilson, Realisation of the basic representations of the Euclidean Lie algebras, to appear. Zbl 0476.17003

[19] J. Lepowsky, Macdonald-type identities, Adv. in Math. 27(1978) 230-234. MR 554353 | Zbl 0388.17003

[20] J. Lepowsky, Generalised Verma modules, loop space cohomology and Macdonald-type identities, Ann. Scient. ENS (4e série) 12(1979) 169-234. Numdam | MR 543216 | Zbl 0414.17007

[21] J. Lepowsky and R.L. Wilson, A Lie-theoretic interpretation and proof of the Rogers-Ramanujan identities, preprint. MR 663415

[22] E. Looijenga, Root systems and elliptic curves, Inv. Math. 38(1976) 17-32. MR 466134 | Zbl 0358.17016

[23] I.G. Macdonald, Affine root systems and Dedekind's n-function, Inv. Math. 15(1972) 92-143. MR 357528 | Zbl 0244.17005

[24] R.V. Moody, A new class of Lie algebras, J. Alg. 10(1968) 211-230. MR 229687 | Zbl 0191.03005

[25] R.V. Moody, Euclidean Lie algebras, Can. J. Math. 21(1969) 1432-1454. MR 255627 | Zbl 0194.34402

[26] P. Slodowy, Chevalley groups over C((t)) and deformations of simply elliptic singularities, RIMS Kyoto University, Japan, 1981. MR 708340