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

Genkai Zhang (Institutionen för matematiska vetenskaper, matematik)
Journal of Functional Analysis (0022-1236). Vol. 269 (2015), 12, p. 3689–3713.
[Artikel, refereegranskad vetenskaplig]

We consider spherical principal series representations of the semisimple Lie group of rank one G=SO(n,1;K)G=SO(n,1;K), K=R,C,HK=R,C,H. There is a family of unitarizable representations πνπν of G for ν in an interval on RR, the so-called complementary series, and subquotients or subrepresentations of G for ν being negative integers. We consider the restriction of (πν,G)(πν,G) under the subgroup H=SO(n−1,1;K)H=SO(n−1,1;K). We prove the appearing of discrete components. The corresponding results for the exceptional Lie group F4(−20)F4(−20) and its subgroup Spin0(8,1)Spin0(8,1) are also obtained.



Denna post skapades 2015-11-17. Senast ändrad 2015-12-30.
CPL Pubid: 225830

 

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Institutioner (Chalmers)

Institutionen för matematiska vetenskaper, matematik (2005-2016)

Ämnesområden

Matematisk analys
Geometri

Chalmers infrastruktur