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Affine Lie algebras and Hecke modular forms. (English) Zbl 0457.17007

MSC:
17B10 Representations of Lie algebras and Lie superalgebras, algebraic theory (weights)
17B65 Infinite-dimensional Lie (super)algebras
11F11 Holomorphic modular forms of integral weight
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[1] Martin Eichler, Introduction to the theory of algebraic numbers and functions, Translated from the German by George Striker. Pure and Applied Mathematics, Vol. 23, Academic Press, New York-London, 1966. · Zbl 0152.19502
[2] Alex J. Feingold and James Lepowsky, The Weyl-Kac character formula and power series identities, Adv. in Math. 29 (1978), no. 3, 271 – 309. · Zbl 0391.17009
[3] I. B. Frenkel and V. G. Kac, Basic representations of affine Lie algebras and dual resonance models, Invent. Math. 62 (1980/81), no. 1, 23 – 66. · Zbl 0493.17010
[4] E. Hecke, Über einen Zusammenhang zwischen elliptischen Modulfunktionen und indefiniten quadratischen Formen, Mathematische Werke, Vandenhoeck and Ruprecht, Göttingen, 1959, pp. 418-427.
[5] V. G. Kac, Simple irreducible graded Lie algebras of finite growth, Izv. Akad. Nauk SSSR Ser. Mat. 32 (1968), 1323 – 1367 (Russian).
[6] V. G. Kac, Infinite-dimensional Lie algebras, and the Dedekind \?-function, Funkcional. Anal. i Priložen. 8 (1974), no. 1, 77 – 78 (Russian).
[7] V. G. Kac, Infinite-dimensional algebras, Dedekind’s \?-function, classical Möbius function and the very strange formula, Adv. in Math. 30 (1978), no. 2, 85 – 136. , https://doi.org/10.1016/0001-8708(78)90033-6 V. G. Kac, An elucidation of: ”Infinite-dimensional algebras, Dedekind’s \?-function, classical Möbius function and the very strange formula”. \?\(_{8}\)\?\textonesuperior \? and the cube root of the modular invariant \?, Adv. in Math. 35 (1980), no. 3, 264 – 273. · Zbl 0431.17009
[8] V. G. Kac, Infinite-dimensional algebras, Dedekind’s \?-function, classical Möbius function and the very strange formula, Adv. in Math. 30 (1978), no. 2, 85 – 136. , https://doi.org/10.1016/0001-8708(78)90033-6 V. G. Kac, An elucidation of: ”Infinite-dimensional algebras, Dedekind’s \?-function, classical Möbius function and the very strange formula”. \?\(_{8}\)\?\textonesuperior \? and the cube root of the modular invariant \?, Adv. in Math. 35 (1980), no. 3, 264 – 273. · Zbl 0431.17009
[9] Eduard Looijenga, Root systems and elliptic curves, Invent. Math. 38 (1976/77), no. 1, 17 – 32. · Zbl 0358.17016
[10] Robert V. Moody, A new class of Lie algebras, J. Algebra 10 (1968), 211 – 230. · Zbl 0191.03005
[11] D. H. Peterson, Kostant-type partition functions (to appear).
[12] V. G. Kac and D. H. Peterson (manuscript in preparation).
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