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Decomposition ofq-deformed Fock spaces

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Abstract

A decomposition of the level-oneq-deformed Fock space representations ofU q(sl n ) is given. It is found that the action ofU′ q(sl n ) on these Fock spaces is centralized by a Heisenberg algebra, which arises from the center of the affine Hecke algebraĤ N in the limitN → ∞. Theq-deformed Fock space is shown to be isomorphic as aU′ q(sl n )-Heisenberg-bimodule to the tensor product of a level-one irreducible highest weight representation ofU′ q(sl n ) 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(sl n ) and from the Heisenberg algebra.

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Authors and Affiliations

  1. Research Institute for Mathematical Sciences, Kyoto University, Sakyo-ku, 606, Kyoto, Japan

    M. Kashiwara & T. Miwa

  2. Department of Mathematics, UC Berkeley, 94720, Berkeley, CA, USA

    E. Stern

Authors
  1. M. Kashiwara
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  2. T. Miwa
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  3. E. Stern
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Kashiwara, M., Miwa, T. & Stern, E. Decomposition ofq-deformed Fock spaces. Selecta Mathematica, New Series 1, 787 (1995). https://doi.org/10.1007/BF01587910

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  • DOI: https://doi.org/10.1007/BF01587910

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