Unitary groups acting on grassmannians associated with a quadratic extension of fields (Q2477876)

The authors study an anisotropic Hermitian space \((V, H)\) of finite dimension over the algebraic closure of a real closed field \(K\). They investigate the action of the unitary group \(U(V,H)\) of isometries of \((V,H)\) on the set \(X_d\) of \(d\)-dimensional \(K\)-subspaces of \(V\). The authors demonstrate that there are infinitely many orbits for the action of \(U\) on \(X_d\).