Conformal Correlation functions in four dimensions from Quaternionic Lauricella system

Correlation functions in Euclidean conformal field theories in four dimensions are expressed as representations of the conformal group $SL(2,\H)$, $\H$ being the field of quaternions, on the configuration space of points. The representations are obtained in terms of Lauricella system for quaternions. It generalizes the two-dimensional case, wherein the $N$-point correlation function is expressed in terms of solutions of Lauricella system on the configuration space of $N$ points on the complex plane, furnishing representation of the conformal group $SL(2,\C)$.