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

Genkai Zhang (Institutionen för matematiska vetenskaper, matematik) ; B Orsted ; J Moellers
Journal of Geometric Analysis (1050-6926). Vol. 26 (2016), 1, p. 118-142.
[Artikel, refereegranskad vetenskaplig]

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.

Nyckelord: Lie groups, representations, H-type groups, invariant differential operators.

Denna post skapades 2014-11-05. Senast ändrad 2016-08-12.
CPL Pubid: 205295


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