Decomposition ofq-deformed Fock spaces

M. Kashiwara ^[1] ; T. Miwa ^[1] ; E. Stern ^[2]
1. [1] Kyoto University
  
  Kyoto University
  
  Kamigyō-ku, Japón
2. [2] Tsinghua-UC Berkeley Shenzhen Institute
  
  Tsinghua-UC Berkeley Shenzhen Institute
  
  Estados Unidos
Localización: Selecta Mathematica, New Series, ISSN 1022-1824, Vol. 1, Nº. 4, 1995, págs. 758-787
Idioma: inglés
DOI: 10.1007/bf01587910
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Resumen
- 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.