1997/10/28 by Weiqiang Wang · 1 citation
Mathematics · #q-alg #math.QA
published as Commun. Contemp. Math., Vol. 1 (1999) 155--199 · Latex, 46 pages
arxiv created 1997/10/28 · arxiv updated 2009/11/30
We construct and study in detail various dual pairs acting on some Fock representations 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.