Symmetry Breaking for Representations of Rank One Orthogonal Groups (Memoirs of the American Mathematical Society) - Softcover

Toshiyuki Kobayashi; Birgit Speh

Softcover

ISBN 10: 147041922X ISBN 13: 9781470419226

Publisher: American Mathematical Society, 2015

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.

About this title

About the Author

Toshiyuki Kobayashi, University of Tokyo, Japan.

Birgit Speh, Cornell University, Ithaca, NY, USA.

Edition details

• Publisher: American Mathematical Society
• Publication date: 2015
• Language: English
• ISBN 10: 147041922X
• ISBN 13: 9781470419226
• Binding: Paperback
• Number of pages: 112