Skip to main content
SpringerLink
Log in
Book cover

Infinite Dimensional Lie Algebras pp 150–164Cite as

Birkhäuser

Integrable highest weight modules over affine Lie algebras. Application to η-function identities

  • Chapter

  • 2533 Accesses

Part of the book series: Progress in Mathematics ((PM,volume 44))

Abstract

In the last three chapters we developed a representation theory of arbitrary Kac-Moody algebras. From now on we turn to the special case of affine Lie algebras.

This is a preview of subscription content, log in via an institution.

Chapter
USD   29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD   84.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD   109.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Learn about institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

Bibliographical notes and comments

  • Macdonald, I. G. [1972] Affine root systems and Dedekind’s ri-function, Inventiones Math. 15 (1972), 91–143.

    Article  MathSciNet  MATH  Google Scholar 

  • Kac, V. G. [1974] Infinite-dimensional Lie algebras and Dedekind’s n-function, Funkt. analys i ego prilozh. 8 (1974), No. 1, 77–78.

    Article  Google Scholar 

  • Kac, V. G. [1974] Infinite-dimensional Lie algebras and Dedekind’s n-function, English translation: Funct. Anal. Appl. 8 (1974), 68–70.

    MATH  Google Scholar 

  • Moody, R. V. [1975] Macdonald identities and Euclidean Lie Algebras, Proc. Amer. Math. Soc, 48 (1975), 43–52.

    MathSciNet  MATH  Google Scholar 

  • Dyson, F. [1972] Missed opportunities, Bull. Amer. Math. Soc. 78 (1972), 635–652.

    Article  MathSciNet  MATH  Google Scholar 

  • Kac, V. G. [1978 A] Infinite-dimensional algebras, Dedekind’s rI-finction, classical Möbious function and the very strange formula, Advances in Math. 30 (1978), 85–136.

    Article  MATH  Google Scholar 

  • Lepowsky, J. [1979] Generalized Verma modules, loop space cohomology and Macdonald-type identities, Ann. Sci. École Norm. Sup. 12 (1979), 169–234.

    MathSciNet  Google Scholar 

  • Feingold, A. J., Lepowsky, J. [1978] The Weyl-Kac character formula and power series identities, Adv. Math. 29 (1978), 271–309.

    MathSciNet  MATH  Google Scholar 

  • Frenkel, I. B., Kac, V. G. [1980] Basic representations of affine Lie algebras and dual resonance models, Invent. Math., 62 (1980), 23–66.

    MathSciNet  MATH  Google Scholar 

  • Kac, V. G. [1980 B] An elucidation of “Infinite dimensional algebras… and the very strange formula”. E81 and the cube root of the modular invariant j, Advances in Math. 35 (1980), 264–273.

    Article  MATH  Google Scholar 

  • Conway, J. H., Norton, S. P. [1979] Monstrous moonshine, Bull. London Math. Soc., 11 (1979), 308–339.

    Article  MathSciNet  MATH  Google Scholar 

  • Kac, V. G., Peterson, D. H. [1983 A] Infinite dimensional Lie algebras, theta functions and modular forms, Advances in Math., 50 (1983).

    Google Scholar 

  • Kostant, B. [1976] On Macdonald’s 77-function formula, the Laplacian and generalized exponents, Advances in Math. 20 (1976), 179–212.

    Article  MathSciNet  MATH  Google Scholar 

  • Goodman, R., Wallach, N. [1983] Structure and unitary cocycle representations of loop groups and the group of diffeomorphisms of the circle, preprint.

    Google Scholar 

  • Garland, H. [1980] The arithmetic theory of loop groups, Publ. Math. IHES 52 (1980), 5–136.

    MathSciNet  MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Mathematics Department, Massachusetts Institute of Technology, 77 Massachusetts Avenue, 02139, Cambridge, MA, USA

    Victor G. Kac

Authors
  1. Victor G. Kac
    View author publications

    You can also search for this author in PubMed Google Scholar

Rights and permissions

Reprints and permissions

Copyright information

© 1983 Springer Science+Business Media New York

About this chapter

Cite this chapter

Kac, V.G. (1983). Integrable highest weight modules over affine Lie algebras. Application to η-function identities. In: Infinite Dimensional Lie Algebras. Progress in Mathematics, vol 44. Birkhäuser, Boston, MA. https://doi.org/10.1007/978-1-4757-1382-4_12

Download citation

  • DOI: https://doi.org/10.1007/978-1-4757-1382-4_12

  • Publisher Name: Birkhäuser, Boston, MA

  • Print ISBN: 978-1-4757-1384-8

  • Online ISBN: 978-1-4757-1382-4

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics

Search

Navigation