Iso-Huygens Deformations of Homogeneous Differential Operators Related to a Special Cone of Rank \({\text{3}}\)

Abstract

We consider iso-Huygens deformations of homogeneous hyperbolic Gindikin operators related to a special cone of rank \({\text{3}}\). The deformations are carried out with the use of Stellmacher--Lagnese and Calogero--Moser potentials. Using the notion of gauge equivalence of operators and the algebraic method of intertwining operators, we write out the fundamental solutions of the deformed operators in closed form and give sufficient conditions for the Huygens principle to hold for these operators in the strengthened or ordinary form.