Fourier transforms of Nilpotent Orbits, limit formulas for reductive lie groups, and wave front cycles of tempered representations

In this thesis, the author gives an explicit formula for the Fourier transform of the canonical measure on a nilpotent coadjoint orbit for GL(n, R). If G is a real, reductive algebraic group, and O C g* = Lie(G)* is a nilpotent coadjoint orbit, a necessary condition is given for 0 to appear in the wave front cycle of a tempered representation. In addition, the coefficients of the wave front cycle of a tempered representation of G are expressed in terms of volumes of precompact submanifolds of certain affine spaces. In the process of proving these results, we obtain several limit formulas for reductive Lie groups.

Department dc:contributor.department

Massachusetts Institute of Technology. Dept. of Mathematics.

Grantor dc:publisher

Massachusetts Institute of Technology

Year dc:date.issued

2011

Author dc:creator

• Harris, Benjamin (Benjamin London)

Advisor dc:contributor.advisor

• David Vogan.

• Mathematics.

Statement dc:rights

• M.I.T. theses are protected by copyright. They may be viewed from this source for any purpose, but reproduction or distribution in any format is prohibited without written permission. See provided URL for inquiries about permission.

Licence dc:rights.uri

• http://dspace.mit.edu/handle/1721.1/7582

Language dc:language.iso

eng

Handle dc:identifier.uri

http://hdl.handle.net/1721.1/67789

OAI identifier oai:identifier

oai:dspace.mit.edu:1721.1/67789