dorsal/arxiv
View SchemaDecomposition of $q$-deformed Fock spaces
| Authors | Masaki Kashiwara, Tetsuji Miwa, Eugene Stern |
|---|---|
| Categories | |
| ArXiv ID | q-alg/9508006 |
| URL | https://arxiv.org/abs/q-alg/9508006 |
Abstract
A decomposition of the level-one $q$-deformed Fock representations of $\uqn$ is given. It is found that the action of $\upqn$ on these Fock spaces is centralized by a Heisenberg algebra, which arises from the center of the affine Hecke algebra $\widehat{H}_N$ in the limit $N \rightarrow \infty$. The $q$-deformed Fock space is shown to be isomorphic as a $\upqn$-Heisenberg-bimodule to the tensor product of a level-one irreducible highest weight representation of $\upqn$ and the Fock representation of the Heisenberg algebra. The isomorphism is used to decompose the $q$-wedging operators, which are intertwiners between the $q$-deformed Fock spaces, into constituents coming from $\upqn$ and from the Heisenberg algebra.
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"abstract": "A decomposition of the level-one $q$-deformed Fock representations of $\\uqn$\nis given. It is found that the action of $\\upqn$ on these Fock spaces is\ncentralized by a Heisenberg algebra, which arises from the center of the affine\nHecke algebra $\\widehat{H}_N$ in the limit $N \\rightarrow \\infty$. The\n$q$-deformed Fock space is shown to be isomorphic as a\n$\\upqn$-Heisenberg-bimodule to the tensor product of a level-one irreducible\nhighest weight representation of $\\upqn$ and the Fock representation of the\nHeisenberg algebra. The isomorphism is used to decompose the $q$-wedging\noperators, which are intertwiners between the $q$-deformed Fock spaces, into\nconstituents coming from $\\upqn$ and from the Heisenberg algebra.",
"arxiv_id": "q-alg/9508006",
"authors": [
"Masaki Kashiwara",
"Tetsuji Miwa",
"Eugene Stern"
],
"categories": [
"q-alg",
"math.QA"
],
"title": "Decomposition of $q$-deformed Fock spaces",
"url": "https://arxiv.org/abs/q-alg/9508006"
},
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