Invariant Differential Operators on H-Type Groups and Discrete Components in Restrictions of Complementary Series of Rank One Semisimple Groups
Möllers J, Ørsted B, Zhang G (2016)
Publication Type: Journal article
Publication year: 2016
Journal
Publisher: Springer Verlag (Germany)
Book Volume: 26
Pages Range: 118-142
Journal Issue: 1
DOI: 10.1007/s12220-014-9540-z
Abstract
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 G1. For this we use the realizations of complementary series representations of G and G1 on Sobolev-type spaces on the nilpotent radicals N and N1 of the minimal parabolics in G and G1, respectively. The groups N and N1 are of H-type and we construct explicitly invariant differential operators between N and N1. 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.
Authors with CRIS profile
Involved external institutions
Aarhus University
Denmark (DK)
Chalmers University of Technology / Chalmers tekniska högskola
Sweden (SE)
Denmark (DK)
Chalmers University of Technology / Chalmers tekniska högskola
Sweden (SE)
How to cite
APA:
Möllers, J., Ørsted, B., & Zhang, G. (2016). Invariant Differential Operators on H-Type Groups and Discrete Components in Restrictions of Complementary Series of Rank One Semisimple Groups. Journal of Geometric Analysis, 26(1), 118-142. https://dx.doi.org/10.1007/s12220-014-9540-z
MLA:
Möllers, Jan, Bent Ørsted, and Genkai Zhang. "Invariant Differential Operators on H-Type Groups and Discrete Components in Restrictions of Complementary Series of Rank One Semisimple Groups." Journal of Geometric Analysis 26.1 (2016): 118-142.
BibTeX: Download