Concerning Transformations of Bases Associated with Unimodular diag(1, −1, −1)-Matrices

Considering a representation space for a group of unimodular diag(1, −1, −1)-matrices, we construct several bases whose elements are eigenfunctions of Casimir infinitesimal operators related to a reduction in the group to some one-parameter subgroups. Finding the kernels of base transformation integral operators in terms of special functions, we consider the compositions of some of these transformations. Since composition is a ‘closed’ operation on the set of base transformations, we obtain some integral relations for the special functions involved in the above kernels.