Vol. 308, No. 2, 2020

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Projective cases for the restriction of the oscillator representation to dual pairs of type I

Sabine J. Lang

Vol. 308 (2020), No. 2, 393–406

For all the irreducible dual pairs of type I (G,G), we analyze the restriction of the oscillator representation as a (𝔤,K)-module, when G is the smaller group. For all (G,G) in the stable range, as well as one more case, the modules obtained are projective. We use the duality correspondence introduced by Howe to analyze these restrictions.

dual pairs, oscillator representation, theta correspondence, duality correspondence
Mathematical Subject Classification 2010
Primary: 11F27
Secondary: 22E50
Received: 23 January 2019
Revised: 16 April 2020
Accepted: 29 April 2020
Published: 9 December 2020
Sabine J. Lang
Department of Mathematics
University of Utah
Salt Lake City, UT
United States