### Abstract

We construct the set of generic representations for parabolic subgroups of the complex orthogonal group SO(2n + 1, C) and show that the set O_{p} of generic representations of an arbitrary parabolic subgroup P ⊂ SO(2n + 1, C) can be explicitly described in terms of unitary representations of some smaller reductive group G_{p}. More precisely, O_{p} is either homeomorphic to the unitary dual of G_{P} or can be written as a disjoint union φ_{Im} _{z1>0,...,Im} _{zh>0} O^{zl,...,zh} _{P}, where h > 0 and each set O^{zl,...,zh} _{P} is homeomorphic to Ĝ_{P}.

Original language | English (US) |
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Pages (from-to) | 259-288 |

Number of pages | 30 |

Journal | Communications in Algebra |

Volume | 24 |

Issue number | 1 |

DOIs | |

State | Published - Jan 1 1996 |

Externally published | Yes |

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### ASJC Scopus subject areas

- Algebra and Number Theory

### Cite this

**Generic representations of parabolic subgroups. Case II-SO(2n+1,C).** / Dvorsky, Alexander.

Research output: Contribution to journal › Article

*Communications in Algebra*, vol. 24, no. 1, pp. 259-288. https://doi.org/10.1080/00927879608825566

}

TY - JOUR

T1 - Generic representations of parabolic subgroups. Case II-SO(2n+1,C)

AU - Dvorsky, Alexander

PY - 1996/1/1

Y1 - 1996/1/1

N2 - We construct the set of generic representations for parabolic subgroups of the complex orthogonal group SO(2n + 1, C) and show that the set Op of generic representations of an arbitrary parabolic subgroup P ⊂ SO(2n + 1, C) can be explicitly described in terms of unitary representations of some smaller reductive group Gp. More precisely, Op is either homeomorphic to the unitary dual of GP or can be written as a disjoint union φIm z1>0,...,Im zh>0 Ozl,...,zh P, where h > 0 and each set Ozl,...,zh P is homeomorphic to ĜP.

AB - We construct the set of generic representations for parabolic subgroups of the complex orthogonal group SO(2n + 1, C) and show that the set Op of generic representations of an arbitrary parabolic subgroup P ⊂ SO(2n + 1, C) can be explicitly described in terms of unitary representations of some smaller reductive group Gp. More precisely, Op is either homeomorphic to the unitary dual of GP or can be written as a disjoint union φIm z1>0,...,Im zh>0 Ozl,...,zh P, where h > 0 and each set Ozl,...,zh P is homeomorphic to ĜP.

UR - http://www.scopus.com/inward/record.url?scp=25844441724&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=25844441724&partnerID=8YFLogxK

U2 - 10.1080/00927879608825566

DO - 10.1080/00927879608825566

M3 - Article

AN - SCOPUS:25844441724

VL - 24

SP - 259

EP - 288

JO - Communications in Algebra

JF - Communications in Algebra

SN - 0092-7872

IS - 1

ER -