### Abstract

Original language | English |
---|---|

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

*Monatshefte für Mathematik*,

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

**Degenerate Principal series representations of SOo(p,p+1).** / Fischer, Veronique; Zhang, Genkai.

Research output: Contribution to journal › Article

*Monatshefte für Mathematik*, vol. 176, no. 1, pp. 87-105. https://doi.org/10.1007/s00605-014-0671-x

}

TY - JOUR

T1 - Degenerate Principal series representations of SOo(p,p+1).

AU - Fischer, Veronique

AU - Zhang, Genkai

PY - 2015/1

Y1 - 2015/1

N2 - 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 \(G\).

AB - 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 \(G\).

UR - http://dx.doi.org/10.1007/s00605-014-0671-x

U2 - 10.1007/s00605-014-0671-x

DO - 10.1007/s00605-014-0671-x

M3 - Article

VL - 176

SP - 87

EP - 105

JO - Monatshefte fur Mathematik

JF - Monatshefte fur Mathematik

SN - 0026-9255

IS - 1

ER -