 A major technique of constructing representations of a reductive Lie group is the method of parabolic induction.In the case of the group SL(2,R), there is up to conjugacy only one proper parabolic subgroup, the Borel subgroup of the upper-triangular matrices of determinant 1.The inducing parameter of an induced principal series representation is a (possibly non-unitrary) character of the multiplicative group of real numbers, which is specified by choosing ε = ± 1 and a complex number μ.