### 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 |
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Pages (from-to) | 87-105 |

Number of pages | 19 |

Journal | Monatshefte für Mathematik |

Volume | 176 |

Issue number | 1 |

Early online date | 17 Sep 2014 |

DOIs | |

Publication status | Published - Jan 2015 |

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## Cite this

Fischer, V., & Zhang, G. (2015). Degenerate Principal series representations of SOo(p,p+1).

*Monatshefte für Mathematik*,*176*(1), 87-105. https://doi.org/10.1007/s00605-014-0671-x