## Tsukuba Journal of Mathematics

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

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

#### 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