A uniqueness result for orthogonal groups as 2-compact groups

Abstract.

Two connected compact Lie groups are isomorphic if and only if their maximal torus normalizers are isomorphic. It is conjectured that this result generalizes to p-compact groups. Here, we prove the generalization for orthogonal groups O(n), the special orthogonal groups SO(2k+ 1) and the spinor groups Spin(2k+ 1) considered as 2-compact groups.