Invariant Differential Operators on H-Type Groups and Discrete Components in Restrictions of Complementary Series of Rank One Semisimple Groups
Journal article, 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

Author

Genkai Zhang

University of Gothenburg

Chalmers, Mathematical Sciences, Mathematics

B Orsted

Aarhus University

Genkai Zhang

Chalmers, Mathematical Sciences, Analysis and Probability Theory

Journal of Geometric Analysis

1050-6926 (ISSN)

Vol. 26 1 118-142

Subject Categories

Mathematics

DOI

10.1007/s12220-014-9540-z

More information

Latest update

11/16/2018