We study tensor products of the spin modules (i.e. the Fermion Fock space representations) for classical (simple or afiine) Kac-Moody Lie algebras. We find out that there are mutually commutant pairs of classical Kac-Moody algebras acting on the spin modules, and describe the irreducible decompositions in terms of Young diagrams. As applications, we obtain a simple explanation of Jimbo-Miwa's branching rule duality (i.e. isomorphisms between coset Virasoro modules) [JM], generalization thereof and the duality of the modular transformation rules of affine Lie algebra characters. © 1989, Japan Society of Clinical Chemistry. All rights reserved.
CITATION STYLE
Hasegawa, K. (1989). spin Module Versions of Weyl’s Reciprocity Theorem for Classical Kac-Moody Lie Algebras -An Application to Branching Rule Duality-. Publications of the Research Institute for Mathematical Sciences, 25(5), 741–828. https://doi.org/10.2977/prims/1195172705
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