Fourier transforms of Nilpotent Orbits, limit formulas for reductive lie groups, and wave front cycles of tempered representations
Author(s)Harris, Benjamin (Benjamin London)
Massachusetts Institute of Technology. Dept. of Mathematics.
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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.
Thesis (Ph. D.)--Massachusetts Institute of Technology, Dept. of Mathematics, 2011.Cataloged from PDF version of thesis.Includes bibliographical references (p. 54-56).
DepartmentMassachusetts Institute of Technology. Dept. of Mathematics.
Massachusetts Institute of Technology