The full asymptotic expansion of analytic torsion on homogeneous spaces

TL;DR

This paper derives explicit full asymptotic expansions of analytic torsion on symmetric and homogeneous spaces, comparing with existing results and applying to lattice representations of Chevalley groups.

Contribution

It provides the first explicit full asymptotic expansion formulas for equivariant complex Ray-Singer torsion on symmetric and complex homogeneous spaces.

Findings

Explicit asymptotic expansions for high powers of line bundles on symmetric spaces.

Comparison with Bismut-Vasserot, Finski, and Puchol results.

Applications to lattice representations of Chevalley groups.

Abstract

The full asymptotic expansion of the equivariant complex Ray-Singer torsion for high powers of line bundles on symmetric spaces is given in an explicit form. In the case of isolated fixed points this expansion is given for general complex homogeneous spaces. Furthermore the full asymptotic expansion is given for the complex analytic torsion form associated to fibrations by projective curves. The expansions are compared with results by Bismut-Vasserot, Finski and Puchol. The results are applied to lattice representations of Chevalley groups.