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Göteborgs universitets publikationer

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

Författare och institution:
Genkai Zhang (Institutionen för matematiska vetenskaper, matematik, Chalmers/GU); B Orsted (-); J Moellers (-)
Publicerad i:
Journal of Geometric Analysis, 26 ( 1 ) s. 118-142
ISSN:
1050-6926
Publikationstyp:
Artikel, refereegranskad vetenskaplig
Publiceringsår:
2016
Språk:
engelska
Fulltextlänk:
Sammanfattning (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 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.
Ämne (baseras på Högskoleverkets indelning av forskningsämnen):
NATURVETENSKAP ->
Matematik
Nyckelord:
Lie groups, representations, H-type groups, invariant differential operators.
Postens nummer:
205295
Posten skapad:
2014-11-05 10:50
Posten ändrad:
2016-08-12 14:08

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