On the rate of exponential decay of coefficients on homogeneous spaces

2025/07/03 by Yves Benoist, Benoist, Yves, Liang, Siwei · 1 citation
Computer Science · Mathematics · #Advanced Mathematical Modeling in Engineering #FOS: Mathematics #Group Theory (math.GR) #Representation Theory (math.RT) #advanced mathematical theories

paper · pdf · doi:10.48550/arxiv.2507.02469

openalex publication_date 2025/07/03 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

For any homogeneous space of a noncompact semisimple Lie group G, we define an exponent with multiple interpretations from representation theory and group theory. As an application, we give a temperedness criterion for L² (G/H) for any closed subgroup H of G, which extends the existing ones of Benoist--Kobayashi for connected subgroups and Lutsko--Weich--Wolf for discrete subgroups.

Citations

• Proper Actions and Representation Theory
• Zariski dense non-tempered subgroups in higher rank of nearly optimal growth
• Polyhedral bounds on the joint spectrum and temperedness of locally symmetric spaces
• Decay estimates for matrix coefficients of unitary representations of semisimple Lie groups
• Dichotomy and measures on limit sets of Anosov groups
• Tempered homogeneous spaces IV
• Tempered homogeneous spaces III
• Critical exponents of normal subgroups in higher rank
• Exotic C*-algebras of geometric groups

Cited by

• The limit cone and bounds on the growth indicator function

Related

• Polyhedral bounds on the joint spectrum and temperedness of locally symmetric spaces
• Decay on homogeneous spaces of reductive type
• Tempered homogeneous spaces II
• Wave Front Sets of Reductive Lie Group Representations III
• Tempered homogeneous spaces IV