Decomposition of $q$-deformed Fock spaces

Details Decomposition of $q$-deformed Fock spaces Decomposition of $q$-deformed Fock spaces

1995-08-14

arxiv.org/abs/q-alg/9508006v1

Mathematics

Quantum Algebra

20 pages, LaTeX file

Scientific paper

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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