# Discrete components in restriction of unitary representations of rank one semisimple Lie groups

@article{Zhang2011DiscreteCI,
title={Discrete components in restriction of unitary representations of rank one semisimple Lie groups},
author={Genkai Zhang},
journal={Journal of Functional Analysis},
year={2011},
volume={269},
pages={3689-3713}
}
• Genkai Zhang
• Published 28 November 2011
• Mathematics
• Journal of Functional Analysis
Restriction of some unitary representations of O(1,N) to symmetric subgroups
• Mathematics
• 2012
We find the complete branching law for the restriction of certain unitary representations of $O(1,n+1)$ to the subgroups $O(1,m+1)\times O(n-m)$, $0\leq m\leq n$. The unitary representations we
Restriction of Most Degenerate Representations of O(1 ,N ) with Respect to Symmetric Pairs
• Mathematics
• 2015
On the occasion of the centennial anniversary of Professor Kunihiko Kodaira's birthday Abstract. We find the complete branching law for the restric- tion of certain unitary representations of O(1 ,n
Restriction of complementary series representations of O(1,N) to symmetric subgroups
• Mathematics
• 2012
We find the complete branching law for the restriction of complementary series representations of $O(1,n+1)$ to the symmetric subgroup $O(1,m+1)\times O(n-m)$, $0\leq m<n$. The decomposition consists
The K-spectrum of symmetry breaking operators and applications
• Mathematics
• 2014
We present a method to calculate intertwining operators between the underlying Harish-Chandra modules of degenerate principal series representations of a reductive Lie group $G$ and a reductive
Restriction to symmetric subgroups of unitary representations of rank one semisimple Lie groups
• Mathematics
• 2013
We consider the spherical complementary series of rank one Lie groups $$H_n={ SO }_0(n, 1; {\mathbb {F}})$$Hn=SO0(n,1;F) for $${\mathbb {F}}={\mathbb {R}}, {\mathbb {C}}, {\mathbb {H}}$$F=R,C,H. We
The compact picture of symmetry-breaking operators for rank-one orthogonal and unitary groups
• Mathematics
Pacific Journal of Mathematics
• 2019
We present a method to calculate intertwining operators between the underlying Harish-Chandra modules of degenerate principal series representations of a reductive Lie group G and a reductive
The compact picture of symmetry breaking operators for rank one orthogonal and unitary groups
• Mathematics
• 2014
We present a method to calculate intertwining operators between the underlying Harish-Chandra modules of degenerate principal series representations of a semisimple Lie group $G$ and a semisimple
Representations of Lie Groups and Supergroups
• Mathematics
• 2013
The workshop focussed on recent developments in the representation theory of group objects in several categories, mostly finite and infinite dimensional smooth manifolds and supermanifolds. The talks
Invariant Differential Operators on H-Type Groups and Discrete Components in Restrictions of Complementary Series of Rank One Semisimple Groups
• Mathematics
• 2016
We explicitly construct a finite number of discrete components in the restriction of complementary series representations of rank one semisimple groups $$G$$G to rank one subgroups $$G_1$$G1. For
New time-changes of unipotent flows on quotients of Lorentz groups
• Siyuan Tang
• Computer Science
Journal of Modern Dynamics
• 2022
A main ingredient of the proof is a stronger version of the branching of the complementary series and a refinement of the works of Ratner and Flaminio–Forni is adequate for the purpose.

## References

SHOWING 1-10 OF 43 REFERENCES
Discrete components of some complementary series representations
• Mathematics
• 2010
We show that the restriction of the complementary series representations of SO(n, 1) to SO(m, 1) (m < n) contains complementary series representations of SO(m, 1) discretely, provided that the
Restriction of some unitary representations of O(1,N) to symmetric subgroups
• Mathematics
• 2012
We find the complete branching law for the restriction of certain unitary representations of $O(1,n+1)$ to the subgroups $O(1,m+1)\times O(n-m)$, $0\leq m\leq n$. The unitary representations we
Discrete decomposability of the restriction ofAq(λ) with respect to reductive subgroups and its applications
SummaryLetG′⊂G be real reductive Lie groups and q a θ-stable parabolic subalgebra of Lie (G) ⊗ ℂ. This paper offers a sufficient condition on (G, G′, q) that the irreducible unitary representation
Unitary Representations of the Lorentz Groups: Reduction of the Supplementary Series under a Noncompact Subgroup
Unitary representations of O(2, 1) belonging to the exceptional class are reduced with respect to the noncompact subgroup O(1, 1). We recover the result that the spectrum of the generator of this
Unitary representations of real reductive groups
• Mathematics
• 2012
We present a finite algorithm for computing the set of irreducible unitary representations of a real reductive group G. The Langlands classification, as formulated by Knapp and Zuckerman, exhibits
Composition series and intertwining operators for the spherical principal series. II
In this paper, we consider the connected split rank one 1 1 Lie group of real type F4 which we denote by F4. We first exhibit F4 as a group of operators on the complexification of A. A. Albert's
Restriction to symmetric subgroups of unitary representations of rank one semisimple Lie groups
• Mathematics
• 2013
We consider the spherical complementary series of rank one Lie groups $$H_n={ SO }_0(n, 1; {\mathbb {F}})$$Hn=SO0(n,1;F) for $${\mathbb {F}}={\mathbb {R}}, {\mathbb {C}}, {\mathbb {H}}$$F=R,C,H. We
Composition series and intertwining operators for the spherical principal series
• Mathematics
• 1972
In this paper, we consider the connected split rank one Lie group of real type F4 which we denote by F4. We first exhibit F4 as a group of operators on the complexification of A. A. Albert's