Symmetry breaking for representations of rank one orthogonal groups
著者
書誌事項
Symmetry breaking for representations of rank one orthogonal groups
（Memoirs of the American Mathematical Society, v. 238,
American Mathematical Society, 2015
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注記
Bibliography: p. 109-110
内容説明・目次
内容説明
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.
目次
Introduction
Symmetry breaking for the spherical principal series representations
Symmetry breaking operators
More about principal series representations
Double 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 operators
Classification of symmetry breaking operators
Residue formulae and functional identities
Image of symmetry breaking operators
Application to analysis on anti-de Sitter space
Application to branching laws of complementary series
Appendix
References
List of symbols
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