Tohoku Mathematical Journal

$K$-finite solutions to conformally invariant systems of differential equations

Anthony C. Kable

Full-text: Open access

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.

Article information

Source
Tohoku Math. J. (2), Volume 63, Number 4 (2011), 539-559.

Dates
First available in Project Euclid: 6 January 2012

Permanent link to this document
https://projecteuclid.org/euclid.tmj/1325886280

Digital Object Identifier
doi:10.2748/tmj/1325886280

Mathematical Reviews number (MathSciNet)
MR2872955

Zentralblatt MATH identifier
1236.22011

Subjects
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]

Keywords
Conformal invariance real flag manifold $K$-finite solution

Citation

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


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References

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  • A. C. Kable, The Heisenberg ultrahyperbolic equation, preprint (2010).