DIFFEOMORPHISM INVARIANT SUBSPACES IN WITTEN 2-GRAVITY ON RXT-2(1 QUANTUM)

We address the role of large diffeomorphisms in Wiaen's 2 + 1 gravity on the manifold R x T-2. In a 'spacelike sector' quantum theory that t reats the large diffeomorphisms as a symmetry, rather than as gauge, t he Hilbert space is shown to contain no non-trivial finite-dimensional subspaces that are invariant under the large diffeomorphisms. Infinit e-dimensional closed invariant subspaces are explicitly constructed, a nd the representation of the large diffeomorphisms is thus shown to be reducible. Comparison is made to Witten's theory on R x Sigma, where Sigma is a higher genus surface.