dorsal/arxiv
View SchemaDuality in infinite dimensional Fock representations
| Authors | Weiqiang Wang |
|---|---|
| Categories | |
| ArXiv ID | q-alg/9710035 |
| URL | https://arxiv.org/abs/q-alg/9710035 |
| Journal | Commun. Contemp. Math., Vol. 1 (1999) 155--199 |
Abstract
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.
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"abstract": "We construct and study in detail various dual pairs acting on some Fock\nrepresentations between a finite dimensional Lie group and a completed infinite\nrank affine algebra associated to an infinite affine Cartan matrix. We give\nexplicit decompositions of a Fock representation into a direct sum of\nirreducible isotypic subspaces with respect to the action of a dual pair,\npresent explicit formulas for the common highest weight vectors and calculate\nthe corresponding highest weights. We further outline applications of these\ndual pairs to the study of tensor products of modules of such an infinite\ndimensional Lie algebra.",
"arxiv_id": "q-alg/9710035",
"authors": [
"Weiqiang Wang"
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"journal_ref": "Commun. Contemp. Math., Vol. 1 (1999) 155--199",
"title": "Duality in infinite dimensional Fock representations",
"url": "https://arxiv.org/abs/q-alg/9710035"
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