Regularity of solutions to a Vekua-type equation on compact Lie groups

TL;DR

This paper establishes conditions for the global hypoellipticity and solvability of Vekua-type operators on compact Lie groups, with a focus on the role of representation properties.

Contribution

It provides necessary and sufficient conditions for hypoellipticity of Vekua-type operators on certain compact Lie groups, advancing understanding of their regularity and solvability.

Findings

Conditions for global hypoellipticity are identified.

Necessity of conditions is shown for groups with non-self-dual representations.

Results on global solvability of the operators are presented.

Abstract

We present sufficient conditions to have global hypoellipticity for a class of Vekua-type operators defined on a compact Lie group. When the group has the property that every non-trivial representation is not self-dual we show that these sufficient conditions are also necessary. We also present results about the global solvability for this class of operators.