The full asymptotic expansion of analytic torsion on homogeneous spaces

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.