Symmetry Breaking for Representations of Rank One Orthogonal Groups 1

Vetenskap & teknik

Symmetry Breaking for Representations of Rank One Orthogonal Groups

Toshiyuki Kobayashi • Birgit Speh

Pocket

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112 sidor
2015

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.

Författare: Toshiyuki Kobayashi, Birgit Speh
Format: Pocket/Paperback
ISBN: 9781470419226
Språk: Engelska
Antal sidor: 112
Utgivningsdatum: 2015-12-30
Förlag: American Mathematical Society