Degenerate Principal series representations of SOo(p,p+1).

Veronique Fischer, Genkai Zhang

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Abstract

For \(p\) odd, the Lie group \(G^\sharp =\mathrm{SO}_0(p+1,p+1)\) has a family of complementary series representations realized on the space of real \((p+1)\times (p+1)\) skew symmetric matrices, similar to the Stein’s complementary series for \(\mathrm{SL}(2n, {\mathbb C})\). We consider their restriction on the subgroup \(G_0=\mathrm{SO}_0(p+1,p)\) and prove that they are still irreducible and is equivalent to (a unitarization of) the principal series representation of \(G=\mathrm{SO}(p+1, p)\), and also irreducible under a maximal parabolic subgroup of \(G\).
Original languageEnglish
Pages (from-to)87-105
Number of pages19
JournalMonatshefte für Mathematik
Volume176
Issue number1
Early online date17 Sep 2014
DOIs
Publication statusPublished - Jan 2015

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Series Representation
Skew symmetric matrix
Parabolic Subgroup
Maximal Subgroup
Odd
Subgroup
Restriction
Series
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Degenerate Principal series representations of SOo(p,p+1). / Fischer, Veronique; Zhang, Genkai.

In: Monatshefte für Mathematik, Vol. 176, No. 1, 01.2015, p. 87-105.

Research output: Contribution to journalArticle

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