K-FINITE SOLUTIONS TO CONFORMALLY INVARIANT SYSTEMS OF DIFFERENTIAL EQUATIONS

摘要

Let G be a connected semisimple linear real Lie group, and Q (resp. K) a real parabolic subgroup (resp. maximal compact subgroup) of G. The space of K-finite solutions to a conformally invariant system of differential equations on a line bundle over the real flag manifold G/Q is studied. The general theory is then applied to certain second order systems on the flag manifold that corresponds to the Heisenberg parabolic subgroup in a split simple Lie group.