Communications in Mathematical Physics

, Volume 104, Issue 4, pp 605–609

Fock representations of the affine Lie algebraA1(1)

  • Minoru Wakimoto

DOI: 10.1007/BF01211068

Cite this article as:
Wakimoto, M. Commun.Math. Phys. (1986) 104: 605. doi:10.1007/BF01211068


The aim of this note is to show that the affine Lie algebraA1(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 wieghtA1(1)-modules for generic (μ,v).

Copyright information

© Springer-Verlag 1986

Authors and Affiliations

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