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Lowest weight representations of some infinite dimensional groups on fock spaces


The results of Kashiwara and Vergne on the decomposition of the tensor products of the ‘Segal-Shale-Weil representation’ are extended to the infinite dimensional case and give all unitary lowest weight representations. Our methods are basically algebraic. When restricted to the finite dimensional case, they yield a new proof.

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Schmidt, M.U. Lowest weight representations of some infinite dimensional groups on fock spaces. Acta Appl Math 18, 59–84 (1990).

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AMS subject classifications (1980)

  • 22E65
  • 22E70

Key words

  • Highest weight modules
  • CCR algebras
  • representation theory