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Tohoku Mathematical Journal
SECOND SERIES VOL. 63, NO. 4
|Tohoku Math. J.|
63 (2011), 539-559
$K$-FINITE SOLUTIONS TO CONFORMALLY INVARIANT SYSTEMS OF DIFFERENTIAL EQUATIONS
Anthony C. Kable
(Received June 3, 2010)
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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