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.
ASJC Scopus subject areas
- Algebra and Number Theory