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

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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 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.

Original languageEnglish (US)
Pages (from-to)259-288
Number of pages30
JournalCommunications in Algebra
Volume24
Issue number1
DOIs
StatePublished - Jan 1 1996
Externally publishedYes

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Parabolic Subgroup
Homeomorphic
Orthogonal Group
Unitary Representation
Reductive Group
Disjoint
Union
Arbitrary

ASJC Scopus subject areas

  • Algebra and Number Theory

Cite this

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

In: Communications in Algebra, Vol. 24, No. 1, 01.01.1996, p. 259-288.

Research output: Contribution to journalArticle

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