Publications Meetings The Profession Membership Programs Math Samplings Policy & Advocacy In the News About the AMS

   
Remote Access
Green Open Access
Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)

 

Fourier inversion on Borel subgroups of Chevalley groups: the symplectic group case


Author: Ronald L. Lipsman
Journal: Trans. Amer. Math. Soc. 260 (1980), 607-622
MSC: Primary 22E50
MathSciNet review: 574803
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

Abstract: In recent papers, the author and J. A. Wolf have developed the Plancherel theory of parabolic subgroups of real reductive Lie groups. This includes describing the irreducible unitary representations, computing the Plancherel measure, and-since parabolic groups are nonunimodular-explicating the (unbounded) Dixmier-Pukanszky operator that appears in the Plancherel formula. The latter has been discovered to be a special kind of pseudodifferential operator. In this paper, the author considers the problem of extending this analysis to parabolic subgroups of semisimple algebraic groups over an arbitrary local field. Thus far he has restricted his attention to Borel subgroups (i.e. minimal parabolics) in Chevalley groups (i.e. split semisimple groups). The results he has obtained are described in this paper for the case of the symplectic group. The final result is (perhaps surprisingly), to a large extent, independent of the local field over which the group is defined. Another interesting feature of the work is the description of the ``pseudodifferential'' Dixmier-Pukanszky operator in the nonarchimedean situation.


References [Enhancements On Off] (What's this?)


Similar Articles

Retrieve articles in Transactions of the American Mathematical Society with MSC: 22E50

Retrieve articles in all journals with MSC: 22E50


Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9947-1980-0574803-9
PII: S 0002-9947(1980)0574803-9
Article copyright: © Copyright 1980 American Mathematical Society