Tohoku Mathematical Journal
2011
December
SECOND SERIES VOL. 63, NO. 4

Tohoku Math. J.
63 (2011), 539-559

Title $K$-FINITE SOLUTIONS TO CONFORMALLY INVARIANT SYSTEMS OF DIFFERENTIAL EQUATIONS

Author Anthony C. Kable

(Received June 3, 2010)
Abstract. 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.

2000 Mathematics Subject Classification. Primary 22E47; Secondary 22E30.
Key words and phrases. Conformal invariance, real flag manifold, $K$-finite solution.

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