ABSTRACT
In this chapter we shall deal with the problem of determining when an analytic representation of a subgroup of a complex analytic group is extendable to the entire group ([12], [25]).
Let L be a complex Lie subgroup of a complex Lie group G, and let ρ be a complex analytic representation of L on a C-linear space V . A representation σ of G is said to be an extension of the representation ρ of L, if the representation space W of σ contains V as a G-stable subspace and σ(x) coincides with ρ(x) on V for all x ∈ L. If the representation ρ of L has such an extension, then we shall simply say that ρ is extendable to G.
