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[x i,y j;i ∈ ℤ andj ∈ ℕ], parametrized by (μ,v) ∈C 2. By corresponding the highest weightΛ μ, υ of πμ, υ to each (μ,ν), the parameter spaceC 2 forms a double cover of the weight spaceCΛ0⊕C −1 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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Communicated by H. Araki
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Wakimoto, M. Fock representations of the affine Lie algebraA (1)1 . Commun.Math. Phys. 104, 605–609 (1986). https://doi.org/10.1007/BF01211068
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DOI: https://doi.org/10.1007/BF01211068