Equivariant Reidemeister torsion on symmetric spaces

Abstract.

We calculate explicitly the equivariant Ray-Singer torsion for all symmetric spaces $G/K$ of compact type with respect to the action of $G$. We show that it equals zero except for the odd-dimensional Graßmannians and the space $\vec{SU}(3)/\vec{SO}(3)$. As a corollary, we classify up to diffeomorphism all isometries of these spaces which are homotopic to the identity; also, we classify their quotients by finite group actions up to homeomorphism.