The second order pole over split quaternions
This is an addition to a series of papers [1, 2, 3, 4], where we develop quaternionic analysis from the point of view of representation theory of the conformal Lie group and its Lie algebra. In this paper we develop split quaternionic analogues of certain results from [4]. Thus we introduce a space of functions Dh ⊕ Da with a natural action of the Lie algebra gl(2, HC) ≊ sl(4, C), decompose Dh ⊕ Da into irreducible components and find the gl(2, Hc)- equivariant projectors onto each of these irreducible components.