Direct limits of low-rank representations of classical groups

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1 Scopus citations


Using Segal-Bargmann model of the oscillator representation, we demonstrate how to organize unipotent representations of the classical groups O(q,q), U(q,q) and Sp(q,q) into compatible families. This construction leads to the irreducible representations of infinite-dimensional direct limit groups O(∞, infin;), U(∞, ∞) and Sp(∞, ∞). We then exhibit some examples of the arising representations and address the question of their admissibility.

Original languageEnglish (US)
Pages (from-to)6011-6022
Number of pages12
JournalCommunications in Algebra
Issue number12
StatePublished - Dec 1 2002
Externally publishedYes

ASJC Scopus subject areas

  • Algebra and Number Theory


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