Tsukuba Journal of Mathematics

On certain conformally invariant systems of differential equations II: Further study of type A systems

Anthony C. Kable

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Abstract

Previously, several families of systems of differential equations that generalize the Heisenberg Laplacian equations were introduced. The study of one of these families is continued here. It is shown that the systems in this family are free of integrability conditions provided that a parameter appearing in the system avoids a certain set of bad values, which is explicitly determined. Properties of polynomial solutions to the systems are investigated and special polynomial solutions involving terminating Lauricella hypergeometric series are given in some cases.

Article information

Source
Tsukuba J. Math., Volume 39, Number 1 (2015), 39-81.

Dates
First available in Project Euclid: 7 August 2015

Permanent link to this document
https://projecteuclid.org/euclid.tkbjm/1438951817

Digital Object Identifier
doi:10.21099/tkbjm/1438951817

Mathematical Reviews number (MathSciNet)
MR3383878

Zentralblatt MATH identifier
1342.35423

Subjects
Primary: 35R03: Partial differential equations on Heisenberg groups, Lie groups, Carnot groups, etc.
Secondary: 35C11: Polynomial solutions 33C65: Appell, Horn and Lauricella functions 22E25: Nilpotent and solvable Lie groups

Keywords
Heisenberg Laplacian Lauricella hypergeometric polynomial systems of differential equations on nilpotent groups module of polynomial solutions

Citation

Kable, Anthony C. On certain conformally invariant systems of differential equations II: Further study of type A systems. Tsukuba J. Math. 39 (2015), no. 1, 39--81. doi:10.21099/tkbjm/1438951817. https://projecteuclid.org/euclid.tkbjm/1438951817


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