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Affine lie algebras and modular forms

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Séminaire Bourbaki vol. 1980/81 Exposés 561–578

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References

  1. M. ADLER and P van MOERBEKE, Completely integrable systems, Kac-Moody Lie algebras and curves, Adv. in Math. 36(1980) 1–44.

    Article  MathSciNet  Google Scholar 

  2. M ADLER and P van MOERBEKE, Linearisation of Hamiltonian systems, Jacobi varieties and representation theory, Adv. in Math. 38(1980) 318–379.

    Article  MATH  MathSciNet  Google Scholar 

  3. J H CONWAY and S P NORTON, Monstrous moonshine, Bull. LMS 11(1979) 308–339.

    MATH  MathSciNet  Google Scholar 

  4. M DEMAZURE, Identités de Macdonald, Sém. Bourbaki 483 (1976).

    Google Scholar 

  5. A FEINGOLD and J LEPOWSKY, The Weyl-Kac character formula and power series identities, Adv. in Math. 29(1978) 271–309.

    Article  MATH  MathSciNet  Google Scholar 

  6. I B FRENKEL, Orbital theory for affine Lie algebras, Inv. Math. (to appear).

    Google Scholar 

  7. I B FRENKEL and V G KAC, Basic representations of affine Lie algebras and dual resonance models, Inv. Math. 62(1980) 23–66.

    Article  MATH  MathSciNet  Google Scholar 

  8. H GARLAND, Dedekind's η-function and the cohomology of infinite-dimensional Lie algebras, PNAS 72(1975) 2493–2495.

    Article  MATH  MathSciNet  Google Scholar 

  9. H GARLAND, The arithmetic theory of loop groups, preprint.

    Google Scholar 

  10. H GARLAND and J LEPOWSKY, Lie algebra homology and the Macdonald-Kac formulas, Inv. Math. 34(1976) 37–76.

    Article  MATH  MathSciNet  Google Scholar 

  11. V G KAC, Simple irreducible graded Lie algebras of finite growth, Math. USSR Izvestiya 2(1968) 1271–1311.

    Article  MATH  MathSciNet  Google Scholar 

  12. V G KAC, Infinite-dimensional Lie algebras and Dedekind's η-function, Funct. Anal. Appl. 8(1974) 68–70.

    Article  MATH  MathSciNet  Google Scholar 

  13. V G KAC, Infinite-dimensional Lie algebras, Dedekind's η-function, classical Möbius formula and the very strange formula, Advances in Math. 30(1978) 85–136.

    Article  MATH  MathSciNet  Google Scholar 

  14. V G KAC, Infinite root systems, representations of graphs and invariant theory, Inv. Math. 56(1980) 57–92.

    Article  MATH  MathSciNet  Google Scholar 

  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.

    Article  MATH  MathSciNet  Google Scholar 

  16. V G KAC and D PETERSON, Affine Lie algebras and Hecke modular forms, Bull. AMS (New Series) 3(1980) 1057–1061.

    MATH  MathSciNet  Google Scholar 

  17. V G KAC and D PETERSON, Infinite-dimensional Lie algebras, theta functions and modular forms, preprint.

    Google Scholar 

  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.

    Google Scholar 

  19. J LEPOWSKY, Macdonald-type identities, Adv. in Math. 27(1978) 230–234.

    Article  MATH  MathSciNet  Google Scholar 

  20. J LEPOWSKY, Generalised Verma modules, loop space cohomology and Macdonald-type identities, Ann. Scient. ENS (4e série) 12(1979) 169–234.

    MATH  MathSciNet  Google Scholar 

  21. J LEPOWSKY and R L WILSON, A Lie-theoretic interpretation and proof of the Rogers-Ramanujan identities, preprint.

    Google Scholar 

  22. E LOOIJENGA, Root systems and elliptic curves, Inv. Math. 38(1976) 17–32.

    Article  MATH  MathSciNet  Google Scholar 

  23. I G MACDONALD, Affine root systems and Dedekind's η-function, Inv. Math. 15(1972) 92–143.

    MathSciNet  Google Scholar 

  24. R V MOODY, A new class of Lie algebras, J. Alg. 10(1968) 211–230.

    Article  MathSciNet  Google Scholar 

  25. R V MOODY, Euclidean Lie algebras, Can. J. Math. 21(1969) 1432–1454.

    MATH  MathSciNet  Google Scholar 

  26. P SLODOWY, Chevalley groups over C((t)) and deformations of simply elliptic singularities, RIMS Kyoto University, Japan, 1981.

    Google Scholar 

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Macdonald, I.G. (1981). Affine lie algebras and modular forms. In: Séminaire Bourbaki vol. 1980/81 Exposés 561–578. Lecture Notes in Mathematics, vol 901. Springer, Berlin, Heidelberg . https://doi.org/10.1007/BFb0097202

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  • DOI: https://doi.org/10.1007/BFb0097202

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  • Print ISBN: 978-3-540-11176-4

  • Online ISBN: 978-3-540-38956-9

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