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Infinite-dimensional algebras, Dedekind’s \(\eta\)-function, classical Möbius function and the very strange formula. (English) Zbl 0391.17010


MSC:

17B65 Infinite-dimensional Lie (super)algebras
11P81 Elementary theory of partitions
11F11 Holomorphic modular forms of integral weight

Citations:

Zbl 0244.17005
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Full Text: DOI

References:

[1] MacDonald, I. G., Affine root systems and Dedekind’s η-function, Invent. Math., 15, 91-143 (1972) · Zbl 0244.17005
[2] Kac, V. G., Infinite-dimensional Lie algebras and Dedekind’s η-function, J. Functional Anal. Appl., 8, 68-70 (1974) · Zbl 0299.17005
[3] Kostant, B., On MacDonald’s η-function formula, the Laplacian and generalized exponents, Advances in Math., 20, 179-212 (1976) · Zbl 0339.10019
[4] Lepowsky, J., MacDonald-type identities, Advances in Math., 27, 230-234 (1978) · Zbl 0388.17003
[5] Kac, V. G., Lie superalgebras, Advances in Math., 26, 8-96 (1977) · Zbl 0366.17012
[6] Kac, V. G., Simple irreducible graded Lie algebras of finite growth, Math. USSR-Izv., 2, 1271-1311 (1968) · Zbl 0222.17007
[7] Kac, V. G., Some properties of contragredient Lie algebras, Trudy MIEM, 5, 48-60 (1969), (in Russian)
[8] Kac, V. G., Characters of typical representations of classical Lie superalgebras, Comm. in Algebra, 5, 889-897 (1977) · Zbl 0359.17010
[9] Kac, V. G., Automorphisms of finite order of semi-simple Lie algebras, J. Functional Anal. Appl., 3, 252-254 (1969), (For a detail exposition see the Helgason’s book Differential geometry, Lie groups and symmetric spaces, Academic Press, 1978) · Zbl 0274.17002
[10] V. G. Kac; V. G. Kac · Zbl 0331.17001
[11] Carlitz, L.; Subbarao, M. V., A simple proof of the quaintuple product identity, (Proc. Amer. Math. Soc., 32 (1972)), 42-44 · Zbl 0234.05005
[12] Vinberg, E. B., Discrete linear groups generated by reflections, Math. USSR-Izv., 5, 1083-1119 (1971) · Zbl 0256.20067
[13] Z̆elobenko, D. P., Compact Lie groups and their representations (1970), Moscow · Zbl 0272.22006
[14] Kac, V. G., An algebraic definition of the compact Lie groups, Trudy MIEM, 5, 36-47 (1969)
[15] Kostant, B., The principal three-dimensional subgroup and the Betti numbers of a complex simple Lie group, Amer. J. Math., 81, 973-1032 (1959) · Zbl 0099.25603
[16] Garland, H.; Lepowsky, J., Lie algebra homology and the MacDonald-Kac formulas, Invent. Math., 34, 37-76 (1976) · Zbl 0358.17015
[17] Shimura, G., Introduction to the arithmetic theory of automorphic functions, (Publ. Math. Soc. Japan, 11 (1971), Univ. Press: Univ. Press Princeton) · Zbl 0872.11023
[18] Bernstein, I. N.; Gelfand, I. M.; Gelfand, S. I., Structure of representations generated by highest weight vectors, J. Functional Anal. Appl., 5, 1-8 (1971) · Zbl 0246.17008
[19] Van Asch, A. G., Modular forms and root systems (1975), preprint · Zbl 0329.10017
[20] Looijenda, E., Root systems and elliptic curves, Invent. Math., 38, 17-32 (1976)
[21] Moody, R. V., A new class of Lie algebras, J. Algebra, 10, 211-230 (1968) · Zbl 0191.03005
[22] Jacobson, N., Lie Algebras (1962), Interscience: Interscience New York · JFM 61.1044.02
[23] H. Garland; H. Garland · Zbl 0424.17009
[24] V. G. Kac, D. A. Kazhdan, J. Lepowsky, and R. L. Wilson; V. G. Kac, D. A. Kazhdan, J. Lepowsky, and R. L. Wilson · Zbl 0476.17003
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