Matrix elements of representations of non-compact groups in a continuous basis

Explicit formulas are obtained by a simple algebraic method for the representations of the finite group transformations ofO(2,1) in a continuous basis when a non-compact generator is diagonalized. Compact and non-compact cases are treated in a unified form and the nature of analytic continuation is determined. The transformation function between the discrete and the continuous bases is also given. These explicit formulas have not been obtained in the literature before.Supported in part by the Air Force Office of Scientific Research, Office of Aerospace Research, U.S. Air Force, under Grant No. AF-AFOSR- 30–67.