Abstract
This chapter explains the Schur orthogonality relations for nonsquare integrable representations of real semisimple linear group. It presents a character table of all irreducible components of principal series representations of G. The chapter reviews the realization of a regular principal series representation. It presents that all regular principal series unitary representation, induced from cuspidal parabolic subgroup, of G is realized on H(G, χ). It presents a definition of a principle series representation of G induced from a given cuspidal parabolic subgroup and state for the admissibility of the representation.
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