This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
N. Bourbaki, Groupes et algèbres de Lie, Chapitres 7, 8, Hermann, Paris, 1975.
A. Feingold and J. Lepowsky, The Weyl-Kac character formula and power series identities, Advances in Math. 29 (1978), 271–309.
I. B. Frenkel, Two constructions of affine Lie algebra representations and the boson-fermion correspondence in quantum field theory, J. Functional Anal. 44 (1981), 259–327.
___, Representations of affine Lie algebras, Hecke modular forms and Korteweg-deVries type equations, Proc. 1981 Rutgers Conference on Lie Algebras and Related Topics, Springer-Verlag Lecture Notes in Mathematics 933 (1982), 71–110.
I. B. Frenkel and V. G. Kac, Basic representations of affine Lie algebras and dual resonance models, Invent. Math. 62 (1980), 23–66.
H. Garland and J. Lepowsky, Lie algebra homology and the Macdonald-Kac formulas, Invent. Math. 34 (1976), 37–76.
V. G. Kac, Infinite-dimensional Lie algebras and Dedekind's η-function, Funkcional. Anal. i Prilozhen. 8 (1974), 77–78; English transl., Functional Anal. Appl. 8 (1974), 68–70.
___, Infinite-dimensional algebras, Dedekind's η-function, classical Möbius function and the very strange formula, Advances in Math. 30 (1978), 85–136.
V. G. Kac, D. A. Kazhdan, J. Lepowsky and R. L. Wilson, Realization of the basic representations of the Euclidean Lie algebras, Advances in Math. 42 (1981), 83–112.
V. G. Kac and D. H. Peterson, Affine Lie algebras and Hecke modular forms, Bull. Amer. Math. Soc. (New Series) 3 (1980), 1057–1061.
J. Lepowsky, Lectures on Kac-Moody Lie algebras, Université Paris VI, spring, 1978.
___, Generalized Verma modules, loop space cohomology and Macdonald-type identities, Ann. Sci. École Norm. Sup. 12 (1979), 169–234.
___, Affine Lie algebras and combinatorial identities, Proc. 1981 Rutgers Conference on Lie Algebras and Related Topics, Springer-Verlag Lecture Notes in Mathematics 933 (1982), 130–156.
J. Lepowsky and R. L. Wilson, Construction of the affine Lie algebra A (1)1 , Comm. Math. Phys. 62 (1978), 43–53.
___, The Rogers-Ramanujan identities: Lie theoretic interpretation and proof, Proc. Nat. Acad. Sci. U.S.A. 78 (1981), 699–701.
___, A Lie theoretic interpretation and proof of the Rogers-Ramanujan identities, Advances in Math. 45 (1982), 21–72.
___, A new family of algebras underlying the Rogers-Ramanu jan identities and generalizations, Proc. Nat. Acad. Sci. U.S.A. 78 (1981), 7254–7258.
___, The structure of standard modules, I: Universal algebras and the Rogers-Ramanujan identities, to appear.
I. G. Macdonald, Affine root systems and Dedekind's η-function, Invent. Math. 15 (1972), 91–143.
G. Segal, Unitary representations of some infinite-dimensional groups, Comm. Math. Phys. 80 (1981), 301–342.
Author information
Authors and Affiliations
Editor information
Rights and permissions
Copyright information
© 1984 Springer-Verlag
About this paper
Cite this paper
Lepowsky, J., Primc, M. (1984). Standard modules for type one affine lie algebras. In: Chudnovsky, D.V., Chudnovsky, G.V., Cohn, H., Nathanson, M.B. (eds) Number Theory. Lecture Notes in Mathematics, vol 1052. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0071544
Download citation
DOI: https://doi.org/10.1007/BFb0071544
Published:
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-12909-7
Online ISBN: 978-3-540-38788-6
eBook Packages: Springer Book Archive