Representation of Generalized Lie Groups and Intertwining Operators

In this paper, using an action of generalized Lie groups on a smooth manifold, we define a representation of a generalized Lie group. Also, we show that there is a Haar measure on a compact generalized Lie group and prove that any finite-dimensional representation of a generalized Lie group is unitary; hence, it is a semisimple representation. Further, we study some properties of intertwining maps and, as a result, we prove Schur’s Lemma for generalized Lie groups.