Decay of matrix coefficients on reductive homogeneous spaces of spherical type

TL;DR

This paper studies how matrix coefficients decay on certain homogeneous spaces of real reductive Lie groups, specifically those of spherical type, providing quantitative decay estimates crucial for representation theory and harmonic analysis.

Contribution

It establishes new quantitative decay rates of matrix coefficients on spherical type homogeneous spaces of real reductive Lie groups, extending understanding in harmonic analysis.

Findings

Derived explicit decay estimates for matrix coefficients.

Extended decay results to a broader class of homogeneous spaces.

Provided tools for applications in representation theory.

Abstract

Let Z be a homogeneous space Z=G/H of a real reductive Lie group G with a reductive subgroup H. The investigation concerns the quantitative decay of matrix coefficients on $Z$ under the assumption that Z is of spherical type, that is, minimal parabolic subgroups have open orbits on Z.