2026-09-20T10:01:40Zhttps://dspace.mit.edu/server/oai/requestoai:dspace.mit.edu:1721.1/677892022-01-13T07:54:35Zcom_1721.1_7582com_1721.1_7581col_1721.1_131022
David Vogan.
Harris, Benjamin (Benjamin London)
Massachusetts Institute of Technology. Dept. of Mathematics.
Massachusetts Institute of Technology. Department of Mathematics
2011-12-19T18:51:39Z
2011-12-19T18:51:39Z
2011
2011
http://hdl.handle.net/1721.1/67789
767740716
Thesis (Ph. D.)--Massachusetts Institute of Technology, Dept. of Mathematics, 2011.
Cataloged from PDF version of thesis.
Includes bibliographical references (p. 54-56).
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.
by Benjamin Harris.
Ph.D.
56 p.
eng
Massachusetts Institute of Technology
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.
http://dspace.mit.edu/handle/1721.1/7582
Mathematics.
Fourier transforms of Nilpotent Orbits, limit formulas for reductive lie groups, and wave front cycles of tempered representations
Thesis
application/pdf
false
Publication
unknown
unknown
<Publication xmlns="https://www.openaire.eu/cerif-profile/1.1/" id="e0c091cc-8844-4400-ba86-be2532d3a1c8">
<Type xmlns="https://www.openaire.eu/cerif-profile/vocab/COAR_Publication_Types">http://purl.org/coar/resource_type/c_1843</Type>
<Language>eng</Language>
<Title>Fourier transforms of Nilpotent Orbits, limit formulas for reductive lie groups, and wave front cycles of tempered representations</Title>
<PublishedIn>
<Publication>
</Publication>
</PublishedIn>
<PublicationDate>2011</PublicationDate>
<Authors>
<Author>
<DisplayName>Harris, Benjamin (Benjamin London)</DisplayName>
<Affiliation>
<OrgUnit>
</OrgUnit>
</Affiliation>
</Author>
</Authors>
<Editors>
</Editors>
<Publishers>
<Publisher>
<DisplayName>Massachusetts Institute of Technology</DisplayName>
<OrgUnit />
</Publisher>
</Publishers>
<License>http://dspace.mit.edu/handle/1721.1/7582</License>
<Keyword>Mathematics.</Keyword>
<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.</Abstract>
<Access xmlns="http://purl.org/coar/access_right"
>
</Access>
</Publication>