Invariant Differential Operators on H-Type Groups and Discrete Components in Restrictions of Complementary Series of Rank One Semisimple Groups
Artikel i vetenskaplig tidskrift, 2016

We explicitly construct a finite number of discrete components in the restriction of complementary series representations of rank one semisimple groups G to rank one subgroups G(1). For this we use the realizations of complementary series representations of G and G(1) on Sobolev-type spaces on the nilpotent radicals N and N-1 of the minimal parabolics in G and G(1), respectively. The groups N and N-1 are of H-type and we construct explicitly invariant differential operators between N and N-1. These operators induce the projections onto the discrete components. Our construction of the invariant differential operators is carried out uniformly in the framework of H-type groups and also works for those H-type groups which do not occur as a nilpotent radical of a parabolic subgroup in a semisimple group.

representations

Lie groups

invariant differential operators.

H-type groups

Författare

Genkai Zhang

Göteborgs universitet

Chalmers, Matematiska vetenskaper, Matematik

B Orsted

Aarhus Universitet

Genkai Zhang

Chalmers, Matematiska vetenskaper, Analys och sannolikhetsteori

Journal of Geometric Analysis

1050-6926 (ISSN)

Vol. 26 1 118-142

Ämneskategorier

Matematik

DOI

10.1007/s12220-014-9540-z

Mer information

Senast uppdaterat

2018-11-16