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Title: Unitary highest weight modules and degenerate principal series
Authors: ZHANG JI
Keywords: degenerate principal series, unitary highest weight module, oscillator representation, distribution, induced representation,harmonic decomposition
Issue Date: 12-Feb-2004
Citation: ZHANG JI (2004-02-12). Unitary highest weight modules and degenerate principal series. ScholarBank@NUS Repository.
Abstract: Let G be the group ~Sp(2n;R) or U(n; n) or O*(4n); P = MN be theSiegel parabolic subgroup of G. Let \omega be the oscillator representation associatedto the dual pair (O(k); Sp(2n;R)) \subseteq Sp(2kn;R); or (U(k);U(n; n)) \subseteq Sp(4kn;R); or (Sp(k); O*(4n)) \subseteq Sp(8kn;R). In this thesis, we apply theresults of Kashiwara and Vergne on harmonic polynomials and give the descriptionof certain N-invariant tempered distributions (under \omega), where Nis the unipotent radical of the Siegel parabolic P. We then embed unitaryhighest weight modules of G into certain degenerate principal series representationsof G induced from finite dimensional representations of P explicitly.
Appears in Collections:Master's Theses (Open)

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