Fock representations of the affine Lie algebraA1(1)
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- Wakimoto, M. Commun.Math. Phys. (1986) 104: 605. doi:10.1007/BF01211068
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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 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 wieghtA1(1)-modules for generic (μ,v).