论文信息 - Decomposition ofq-deformed Fock spaces

Decomposition ofq-deformed Fock spaces

A decomposition of the level-oneq-deformed Fock space representations ofUq(sln) is given. It is found that the action ofU′q(sln) on these Fock spaces is centralized by a Heisenberg algebra, which arises from the center of the affine Hecke algebraĤN in the limitN → ∞. Theq-deformed Fock space is shown to be isomorphic as aU′q(sln)-Heisenberg-bimodule to the tensor product of a level-one irreducible highest weight representation ofU′q(sln) and the Fock representation of the Heisenberg algebra. The isomorphism is used to decompose theq-wedging operators, which are intertwiners between theq-deformed Fock spaces, into constituents coming fromU′q(sln) and from the Heisenberg algebra.

Masaki Kashiwara | Tetsuji Miwa | Eugene Stern

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