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Symmetry breaking for representations of rank one orthogonal groups

Author: Toshiyuki Kobayashi; Birgit Speh; American Mathematical Society,
Publisher: Providence, Rhode Island : American Mathematical Society, 2015. ©2015
Series: Memoirs of the American Mathematical Society, no. 1126.
Edition/Format:   eBook : Document : EnglishView all editions and formats
Summary:
The authors give a complete classification of intertwining operators (symmetry breaking operators) between spherical principal series representations of G=O(n+1,1) and G'=O(n,1). They construct three meromorphic families of the symmetry breaking operators, and find their distribution kernels and their residues at all poles explicitly. Symmetry breaking operators at exceptional discrete parameters are thoroughly  Read more...
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Genre/Form: Electronic books
Additional Physical Format: Print version:
Kobayashi, Toshiyuki, 1962-
Symmetry breaking for representations of rank one orthogonal groups.
Providence, Rhode Island : American Mathematical Society, 2015
(DLC) 2015027247
(OCoLC)916408495
Material Type: Document, Internet resource
Document Type: Internet Resource, Computer File
All Authors / Contributors: Toshiyuki Kobayashi; Birgit Speh; American Mathematical Society,
ISBN: 9781470426156 1470426153 147041922X 9781470419226
OCLC Number: 920024642
Notes: "Volume 238, number 1126 (fourth of 6 numbers), November 2015"
Description: 1 online resource (v, 112 pages) : illustrations.
Contents: IntroductionSymmetry breaking for the spherical principal series representationsSymmetry breaking operatorsMore about principal series representationsDouble coset decomposition $P'\setminus G/P$Differential equations satisfied by the distribution kernels of symmetry breaking operators $K$-finite vectors and regular symmetry breaking operators $\widetilde {\mathbb {A}} _{\lambda , \nu }$Meromorphic continuation of regular symmetry breaking operators ${K}_{<!-- -->{\lambda },{\nu }}^{\mathbb {A}}$Singular symmetry breaking operator $\widetilde {\mathbb {B}} _{\lambda ,\nu }$Differential symmetry breaking operatorsClassification of symmetry breaking operatorsResidue formulae and functional identitiesImage of symmetry breaking operatorsApplication to analysis on anti-de Sitter spaceApplication to branching laws of complementary seriesAppendixReferencesList of symbols
Series Title: Memoirs of the American Mathematical Society, no. 1126.
Responsibility: Toshiyuki Kobayashi, Birgit Speh.

Abstract:

The authors give a complete classification of intertwining operators (symmetry breaking operators) between spherical principal series representations of $G=O(n+1,1)$ and $G'=O(n,1)$. They construct  Read more...

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