Tohoku Mathematical Journal
- Tohoku Math. J. (2)
- Volume 63, Number 4 (2011), 539-559.
$K$-finite solutions to conformally invariant systems of differential equations
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.
Tohoku Math. J. (2), Volume 63, Number 4 (2011), 539-559.
First available in Project Euclid: 6 January 2012
Permanent link to this document
Digital Object Identifier
Mathematical Reviews number (MathSciNet)
Zentralblatt MATH identifier
Primary: 22E47: Representations of Lie and real algebraic groups: algebraic methods (Verma modules, etc.) [See also 17B10]
Secondary: 22E30: Analysis on real and complex Lie groups [See also 33C80, 43-XX]
Kable, Anthony C. $K$-finite solutions to conformally invariant systems of differential equations. Tohoku Math. J. (2) 63 (2011), no. 4, 539--559. doi:10.2748/tmj/1325886280. https://projecteuclid.org/euclid.tmj/1325886280