  We consider ADE-type (2, 0) theory on a family of flat six-tori endowed with
flat Sp(4) connections coupled to the R-symmetry. Our main objects of interest
are the components of the `partition vector' of the theory. These constitute an
element of a certain finite dimensional vector space, carrying an irreducible
representation of a discrete Heisenberg group related to the 't Hooft fluxes of
the theory. Covariance under the SL_6(Z) mapping class group of a six-torus
amounts to a certain automorphic transformation law for the partition vector,
which we derive. Because of the absence of a Lagrangian formulation of (2, 0)
theory, this transformation property is not manifest, and gives useful
non-trivial constraints on the partition vector. As an application, we derive a
shifted quantization law for the spatial momentum of (2, 0) theory on a
space-time of the form R x T5. This quantization law is in agreement with an
earlier result based on the relationship between (2, 0) theory and maximally
supersymmetric Yang-Mills theory together with certain geometric facts about
gauge bundles.
