Projectors separating spectra for $L^2$ on symmetric spaces $GL(n,\C)/GL(n,\R)$

TL;DR

This paper explicitly constructs orthogonal projectors that decompose the spectrum of the $L^2$ space on the symmetric space $GL(n,C)/GL(n,R)$ into uniform parts, enhancing understanding of its spectral structure.

Contribution

It provides explicit formulas for orthogonal projectors that separate the spectrum of $L^2$ on the symmetric space into distinct uniform components, clarifying spectral decomposition.

Findings

Spectrum of $L^2$ on $GL(n,C)/GL(n,R)$ has $[n/2]$ types.

Constructed explicit orthogonal projectors for spectral separation.

Enhanced understanding of spectral decomposition on pseudo-Riemannian symmetric spaces.

Abstract

The Plancherel decomposition of $L^2$ on a pseudo-Riemannian symmetric space $GL(n,C)/GL(n,R)$ has spectrum of $[n/2]$ types. We write explicitly orthogonal projectors separating spectrum into uniform pieces