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The present paper is dedicated to the proof of dispersive estimates onstratified Lie groups of step 2, for the linear Schr\"odinger equationinvolving a sublaplacian. It turns out that the propagator behaves like a waveoperator on a space of the same dimension p as the center of the group, andlike a Schr\"odinger operator on a space of the same dimension k as the radicalof the canonical skew-symmetric form, which suggests a decay with exponant-(k+p-1)/2. In this article, we identify a property of the canonicalskew-symmetric form under which we establish optimal dispersive estimates withthis rate. The relevance of this property is discussed through severalexamples.

Dispersive estimates for the Schr\"odinger operator on step 2 stratified Lie groups