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

Veronique Fischer, Genkai Zhang

Research output: Contribution to journalArticle

### 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 language English 87-105 19 Monatshefte für Mathematik 176 1 17 Sep 2014 https://doi.org/10.1007/s00605-014-0671-x Published - Jan 2015

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Series Representation
Skew symmetric matrix
Parabolic Subgroup
Maximal Subgroup
Odd
Subgroup
Restriction
Series
Family

### Cite this

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

Research output: Contribution to journalArticle

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