\(K\)-finite solutions to conformally invariant systems of differential equations (Q765666)

Let \(G\) be a connected semisimple linear real Lie group; \(Q\) a real parabolic subgroup and \(K\) a maximal compact subgroup. In this paper the author studies the space of \(K\)-finite solutions to a conformal invariant system of differential equations on a line bundle over the real flag manifold \(G/Q\). In particular, for one such system of second order in type \(C\) the author obtains an explicit description of the \(K\)-module structure on the space of \(K\)-finite solutions. In another type the author obtains various general results for second order systems on the flag manifold that corresponds to the Heisenberg parabolic subgroup in a split simple group.