Fourier Transforms of Nilpotent, Coadjoint Orbits for GL(n,R)
Benjamin Harris
TL;DR
This paper provides an explicit formula for the Fourier transform of measures on nilpotent coadjoint orbits for GL(n,R), and discusses limit formulas for reductive Lie groups with new proofs of classical results.
Contribution
It introduces a new explicit formula for Fourier transforms on nilpotent orbits and offers novel proofs for classical limit formulas in reductive Lie groups.
Findings
Explicit Fourier transform formula for nilpotent coadjoint orbits
New proofs of Rao and Harish-Chandra limit formulas
Results on limit formulas for reductive Lie groups
Abstract
The main result of this paper is an explicit formula for the Fourier transform of the canonical measure on a nilpotent coadjoint orbit for GL(n,R). This paper also includes some results on limit formulas for reductive Lie groups including new proofs of classical limit formulas of Rao and Harish-Chandra.
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Taxonomy
TopicsAdvanced Algebra and Geometry · Algebraic Geometry and Number Theory · Finite Group Theory Research