Abstract
This is an account of some of my recent work [2,3] which has involved applications of vertex operators to Kac-Moody Lie theory. For V the basic A1 (1)-module in the principal realization given by Lepowsky and Wilson [13], one may use vertex operators to describe the decomposition \( V \otimes \;V = S(V)\; \oplus \;A(V) \) of V ⊗ V into symmetric tensors S(V) and antisymmetric tensors A(V). This turns out to be precisely the decomposition of V ⊗ V into two “strings” of level two standard A1 (1)-modules which I found in [1].This result has a remarkable application to the construction of the hyperbolic algebra F with Dynkin diagram
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Partially supported by the National Science Foundation through the Mathematical Sciences Research Institute
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Feingold, A.J. (1985). Some Applications of Vertex Operators to Kac-Moody Algebras. In: Lepowsky, J., Mandelstam, S., Singer, I.M. (eds) Vertex Operators in Mathematics and Physics. Mathematical Sciences Research Institute Publications, vol 3. Springer, New York, NY. https://doi.org/10.1007/978-1-4613-9550-8_9
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