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In these notes we discuss the self-reducibility property of the Weil representation. We explain how to use this property to obtain sharp estimates of certain higher-dimensional exponential sums which originate from the theory of quantum chaos. As a result, we obtain the Hecke quantum unique ergodicity theorem for a generic linear symplectomorphism A of the torus \mathbbT = \mathbbR2N/\mathbbZ2N.{\mathbb{T} = \mathbb{R}}^{2N}/{\mathbb{Z}}^{2N}.

Notes on the Self-Reducibility of the Weil Representation and Higher-Dimensional Quantum Chaos