Equivariant Reidemeister torsion on symmetric spaces (Q1359516)

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 SU(3)/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.