On certain conformally invariant systems of differential equations. II: Further study of type A systems. (English) Zbl 1342.35423

Kable, Anthony C.

Tsukuba J. Math. 39, No. 1, 39-81 (2015).

The author studies a family of system of differential equations where the operators are generalizations of the Heisenberg Laplacians associated to special linear and special unitary groups. Continuing a previous work, the author determines the spectrum of some operator studied before, shows that under some restrictions the systems are free of integrability conditions and exhibit some explicit polynomial solutions in certain cases.
For Part I see [the author, New York J. Math. 19, 189–251 (2013; Zbl 1276.35144)].

Reviewer: Isolda E. Cardoso (Rosario)

MSC:

35R03	PDEs on Heisenberg groups, Lie groups, Carnot groups, etc.
35C11	Polynomial solutions to PDEs
33C65	Appell, Horn and Lauricella functions
22E25	Nilpotent and solvable Lie groups

Keywords:

systems of differential equations; Heisenberg group; Heisenberg Laplacian

Citations:

Zbl 1276.35144