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Symmetry Breaking for Representations of Rank One Orthogonal Groups

Symmetry Breaking for Representations of Rank One Orthogonal Groups (Paperback)

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Synopsis

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 studied. The authors obtain closed formulae for the functional equations which the composition of the symmetry breaking operators with the Knapp--Stein intertwining operators of $G$ and $G'$ satisfy, and use them to determine the symmetry breaking operators between irreducible composition factors of the spherical principal series representations of $G$ and $G'$. Some applications are included.

Science & MathematicsMathematicsAlgebraScience & MathematicsMathematicsCalculus & mathematical analysisFunctional analysis & transforms Publisher: American Mathematical Society Publication Date: 30/10/2015 ISBN-13: 9781470419226  Details: Type: Paperback Format: Books
Availability: To Order. Estimated despatch in 1-3 weeks.  

Toshiyuki Kobayashi, University of Tokyo, Japan. Birgit Speh, Cornell University, Ithaca, NY, USA.

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