Analytic torsion and L^2-torsion of compact locally symmetric manifolds

TL;DR

This paper investigates the asymptotic behavior of analytic torsion and L^2-torsion in compact locally symmetric manifolds, focusing on representations derived from the isometry group and their highest weights.

Contribution

It provides new insights into the asymptotic properties of analytic torsion for sequences of representations related to symmetric spaces.

Findings

Asymptotic formulas for analytic torsion are derived.

Behavior of L^2-torsion under representation sequences is characterized.

Connections between torsion invariants and representation theory are established.

Abstract

In this paper we study the analytic torsion and the $L^2$-torsion of compact locally symmetric manifolds. We consider the analytic torsion with respect to representations of the fundamental group which are obtained by restriction of irreducible representations of the group of isometries of the underlying symmetric space. The main purpose is to study the asymptotic behavior of the analytic torsion with respect to sequences of representations associated to rays of highest weights.