Duality in infinite dimensional Fock representations
نویسنده
چکیده
We construct and study in detail various dual pairs acting on some Fock spaces between a finite dimensional Lie group and a completed infinite rank affine algebra associated to an infinite affine Cartan matrix. We give explicit decompositions of a Fock representation into a direct sum of irreducible isotypic subspaces with respect to the action of a dual pair, present explicit formulas for the common highest weight vectors and calculate the corresponding highest weights. We further outline applications of these dual pairs to the study of tensor products of modules of such an infinite dimensional Lie algebra.
منابع مشابه
Infinite-dimensional Lie Algebras, Representations, Hermitian Duality and the Operators of Stochastic Calculus
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