Fourier transforms of Nilpotent Orbits, limit formulas for reductive lie groups, and wave front cycles of tempered representations
Name
767740716-MIT.pdf
Description
Full printable version
Size
2.09 MB
Format
Adobe PDF
Checksum (MD5)
54c959b17514f759f57725efe10df5dd
Author(s)
Harris, Benjamin (Benjamin London)
Advisor(s)
David Vogan.
Date Issued
2011
Publisher
Massachusetts Institute of Technology
Abstract
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.
Description
Thesis (Ph. D.)--Massachusetts Institute of Technology, Dept. of Mathematics, 2011.
Cataloged from PDF version of thesis.
Includes bibliographical references (p. 54-56).
Subjects
Mathematics.
MIT Department
Massachusetts Institute of Technology. Department of Mathematics
Terms of Use
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.
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.
Persistent DSpace Link
