Invariant differential operators on the Grassmann manifold \(G_{2,n- 1}(\mathbb{C})\) (Q1261615)

Let \(Gr(2n-1)\) be the Grassmann manifold of complex 2 dimensional planes through the origin in \(\mathbb{C}^{n+1}\); this is a rank 2 symmetric space. Let \(\mathcal D\) be the algebra of invariant scalar valued linear differential operators on \(Gr(2,n-1)\); \(\mathcal D\) is generated by two different operators \(\widehat{\Delta}_ 0\) and \(\widehat{\Delta}_ 1\). The authors exhibit a simultaneous eigenspace decomposition for \(L^ 2(Gr(2,n-1))\) for these two operators.