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March 29, 2026Open Access

Fourier Transforms of Nilpotent Coadjoint Orbits for GL(n,R)

Key Points

The main aim is to establish an explicit formula for the Fourier transform of the canonical measure on nilpotent coadjoint orbits for GL(n, R).
Derivation of explicit Fourier transform formulas
Examination of nilpotent coadjoint orbits
Proof of limit formulas for reductive Lie groups
An explicit formula for the Fourier transform was successfully derived
New proofs of classical limit formulas by Rao and Harish-Chandra were presented

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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