Supersymmetry of Rotating Branes

We present a new 1/8 supersymmetric intersecting M-brane solution of D=11 supergravity with two independent rotation parameters. The metric has a non-singular event horizon and the near-horizon geometry is adS3×S×S×E (just as in the non-rotating case). We also present a method of determining the isometry supergroup of supergravity solutions from the Killing spinors and use it to show that for the near horizon solution it is D(2|1, α)× D(2|1, α) where α is the ratio of the two 3-sphere radii. We also consider various dimensional reductions of our solution, and the corresponding effect of these reductions on the Killing spinors and the isometry supergroups. ∗Permanent address: Department of Physics, McGill University, Montréal, PQ, H3A 2T8, Canada †Permanent address: DAMTP, University of Cambridge, Cambridge CB3 9EW, U.K.