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Decomposition ofq-deformed Fock spaces

Decomposition of \(q\)-deformed Fock spaces
Authors: Kashiwara, M.; Miwa, T.; Stern, E.;

Decomposition ofq-deformed Fock spaces

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.

20 pages, LaTeX file

Keywords

level-one \(q\)-deformed Fock space representations, decomposition, quantum groups, Heisenberg algebra, Quantum groups (quantized enveloping algebras) and related deformations, highest weight representation, \(q\)-wedging operators, intertwiners, Mathematics - Quantum Algebra, FOS: Mathematics, Quantum Algebra (math.QA), Quantum groups and related algebraic methods applied to problems in quantum theory, Fock representation

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selected citations
These citations are derived from selected sources.
This is an alternative to the "Influence" indicator, which also reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
BIP!Citations provided by BIP!
popularity
This indicator reflects the "current" impact/attention (the "hype") of an article in the research community at large, based on the underlying citation network.
BIP!Popularity provided by BIP!
influence
This indicator reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
BIP!Influence provided by BIP!
impulse
This indicator reflects the initial momentum of an article directly after its publication, based on the underlying citation network.
BIP!Impulse provided by BIP!
43
Top 10%
Top 10%
Top 10%
Green