Communications in Mathematical Physics

, Volume 104, Issue 4, pp 605–609 | Cite as

Fock representations of the affine Lie algebraA 1 (1)

  • Minoru Wakimoto
Article

Abstract

The aim of this note is to show that the affine Lie algebraA 1 (1) has a natural family πμ, υ,v of Fock representations on the spaceC[xi,yj;i ∈ ℤ andj ∈ ℕ], parametrized by (μ,v) ∈C2. By corresponding the highest weightΛμ, υ of πμ, υ to each (μ,ν), the parameter spaceC2 forms a double cover of the weight spaceCΛ0C1 with singularities at linear forms of level −2; this number is (−1)-times the dual Coxeter number. Our results contain explicit realizations of irreducible non-integrable highest wieghtA 1 (1) -modules for generic (μ,v).

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References

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Copyright information

© Springer-Verlag 1986

Authors and Affiliations

  • Minoru Wakimoto
    • 1
  1. 1.Department of Mathematics, Faculty of ScienceHiroshima UniversityHiroshimaJapan

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