  Strichartz estimates are a manifestation of a dispersion phenomenon,
exhibited by certain partial differential equations, which is detected by
suitable Lebesgue space norms. In most cases the evolution propagator $U(t)$ is
a one parameter group of unitary operators. Motivated by the importance of
decay estimates in group representation theory and ergodic theory,
Strichartz-type estimates seem worth investigating when $U(t)$ is replaced by a
unitary representation of a non-compact Lie group, the group element playing
the role of time. Since the Schr\"odinger group is a subgroup of the metaplectc
group, the case of the metaplectic or oscillatory representation is of special
interest in this connection. We prove uniform weak-type sharp estimates for
matrix coefficients and Strichartz estimates for that representation. The
crucial point is the choice of function spaces able to detect such a dispersive
effect, which in general will depend on the given group action. The relevant
function spaces here turn out to be the so-called modulation spaces from
Time-frequency Analysis in Euclidean space, and Lebesgue spaces with respect to
Haar measure on the metaplectic group. The proofs make use in an essential way
of the covariance of the Wigner distribution with respect to the metaplectic
representation.
