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.
Toshiyuki Kobayashi
Symmetry Breaking for Representations of Rank One Orthogonal Groups [PDF ebook]
Symmetry Breaking for Representations of Rank One Orthogonal Groups [PDF ebook]
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Format PDF ● Halaman-halaman 112 ● ISBN 9781470426156 ● Penerbit American Mathematical Society ● Muat turun 3 kali ● Mata wang EUR ● ID 8057031 ● Salin perlindungan Adobe DRM
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