Lie algebras and special functions related to the isotropic cone

In this paper, we discuss the relationship between some maximal subalgebras of the Lie algebra of the proper three-dimensional Lorentz group $G$ and some special functions: Bessel and Bessel–Clifford functions, wave Coulomb functions, the Appel hypergeometric function $F_1$, etc. The kernels of integral operators in the space of representations are expressed in terms of the function introduced by the authors. For this function, we derive continual addition theorems, which, in turn, lead to integral formulas for special functions. We briefly discuss similar results related to groups similar to $G$.