Fock representations of the affine Lie algebraA
1
(1) |
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Authors: | Minoru Wakimoto |
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Institution: | (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 algebraA
1
(1)
has a natural family ![pgr](/content/u761v42n2uk16318/xxlarge960.gif) , ,v of Fock representations on the spaceCx
i,y
j;i andj ], parametrized by ( ,v) C
2. By corresponding the highest weight
, of ![pgr](/content/u761v42n2uk16318/xxlarge960.gif) , to each ( , ), the parameter spaceC
2 forms a double cover of the weight spaceC 0 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 ( ,v). |
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Keywords: | |
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