Classification of invariant valuations on the quaternionic plane (Q457606)

The authors describe the orbit space of the action of the group \(\mathrm{Sp}(2)\mathrm{Sp}(1)\) on the real Grassmann manifolds \(\mathrm{Gr}_k(\mathbb H^2)\) in terms of certain quaternionic matrices of Moore rank not larger than 2. They give also a complete classification of valuations on the quaternionic plane \(\mathbb H^2\) which are invariant under the action of the group \(\mathrm{Sp}(2)\mathrm{Sp}(1)\).