\(K\)-finite solutions to conformally invariant systems of differential equations
type: Item
instance of: scholarly article
title: \(K\)-finite solutions to conformally invariant systems of differential equations
zbMATH Open document ID: 1236.22011
author: Anthony C. Kable
published in: Tôhoku Mathematical Journal. Second Series
publication date: 2012-03-21T00:00:00Z
review text: Let \(G\) be a connected semisimple linear real Lie group; \(Q\) a real parabolic subgroup and \(K\) a maximal compact subgroup. In this paper the author studies the space of \(K\)-finite solutions to a conformal invariant system of differential equations on a line bundle over the real flag manifold \(G/Q\). In particular, for one such system of second order in type \(C\) the author obtains an explicit description of the \(K\)-module structure on the space of \(K\)-finite solutions. In another type the author obtains various general results for second order systems on the flag manifold that corresponds to the Heisenberg parabolic subgroup in a split simple group.
reviewed by: Volodymyr Mazorchuk
Mathematics Subject Classification ID: 22E47
Mathematics Subject Classification ID: 22E30
zbMATH DE Number: 6016706
zbMATH Keywords: conformal invariance
zbMATH Keywords: real flag manifold
zbMATH Keywords: solution
zbMATH Keywords: differential equation
zbMATH Keywords: Heisenberg subgroup
zbMATH Keywords: Lie group
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.2748/tmj/1325886280
OpenAlex ID: W2071398725
cites work: Conformally invariant systems of differential equations and prehomogeneous vector spaces of Heisenberg parabolic type
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cites work: Q3225757
cites work: Symmetry in the functional equation of a local zeta distribution
DOI: 10.2748/TMJ/1325886280
description: scientific article; zbMATH DE number 6016706