Abstract
We announce the main results of our paper [5] on the structure of the standard modules for the affine Lie algebra A1 (1) in the “homogeneous picture”. This study, already begun in [4], was stimulated by the investigation [6] of the structure of the standard A1 (1) -modules in the “principal picture”. For detailed background and references, these papers and [1], [2], [7] and [8] should be consulted.
Partially supported by the National Science Foundation through the Mathematical Sciences Research Institute.
Partially supported by NSF grants MCS 80–03000 and MCS 83–01664.
Partially supported by the Institute for Advanced Study and Samoupravna interesna zajednica za znanstveni rad SRH-SIZ VI.
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References
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.
I.B. Frenkel and V.G. Kac, Basic representations of affine Lie algebras and dual resonance models, Invent. Math. 62 (1980), 23–66.
J. Lepowsky and S. Milne, Lie algebraic approaches to classical partition identities, Advances in Math. 29 (1978), 15–59.
J. Lepowsky and M. Prime, Standard modules for type one affine Lie algebras, Number Theory, New York, 1982, Springer-Verlag Lecture Notes in Mathematics 1052 (1984), 194–251.
J. Lepowsky and M. Primc, Structure of the standard modules for the affine Lie algebra A1 (1), to appear.
J. Lepowsky and R.L. Wilson, A new family of algebras underlying the Rogers-Ramanujan identities and generalizations, Proc. Nat. Acad. Sci. U.S.A. 78 (1981), 7254–7258.
J. Lepowsky and R.L. Wilson, The structure of standard modules, I: Universal algebras and the Rogers-Ramanujan identities, Invent. Math. (1984).
G. Segal, Unitary representations of some infinite-dimensional groups, Comm. Math. Phys. 80 (1981), 301–342.
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Lepowsky, J., Primc, M. (1985). Structure of the Standard Modules for the Affine Lie Algebra A1 (1) in the Homogeneous Picture. In: Lepowsky, J., Mandelstam, S., Singer, I.M. (eds) Vertex Operators in Mathematics and Physics. Mathematical Sciences Research Institute Publications, vol 3. Springer, New York, NY. https://doi.org/10.1007/978-1-4613-9550-8_7
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DOI: https://doi.org/10.1007/978-1-4613-9550-8_7
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