Finite Dimensional Representations of a Semi-Simple Lie Group

Abstract

Let G be a connected semi-simple Lie group with finite center, say — then it is not necessarily the case that G possesses enough finite dimensional representations to separate points (cf. 3.1.1). In fact G will, in general, admit no non-trivial finite dimensional unitary representations (cf. number 4.3.2). Nevertheless, despite these apparently discouraging facts, the finite dimensional representations of G are important — this will be elaborated on below.