Fock representations of the affine Lie algebraA 1 (1) |
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Authors: | Minoru Wakimoto |
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Affiliation: | (1) Department of Mathematics, Faculty of Science, Hiroshima University, 730 Hiroshima, Japan |
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Abstract: | The aim of this note is to show that the affine Lie algebraA1(1) has a natural family , ,v of Fock representations on the spaceC[xi,yj;i andj ], parametrized by (,v) C2. By corresponding the highest weight, of , to each (,), the parameter spaceC2 forms a double cover of the weight spaceC0C –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 (,v). |
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