  We study sums of Hecke eigenvalues of Hecke-Maass cusp forms for the group
$\mathrm{SL}(n,\mathbb Z)$, with general $n\geq 3$, over certain short
intervals under the assumption of the generalised Lindel\"of hypothesis and a
slightly stronger upper bound concerning the exponent towards the
Ramanujan-Petersson conjecture that is currently known. In particular, in this
case we evaluate the second moment of the sums in question asymptotically.
