INTERTWINING-OPERATORS FOR EXPONENTIAL LI E-GROUPS

Let G be an exponential Lie group with Lie algebra g. Let f be in the dual g of g. If h1 and h2 are two polarizations at f which satisfy Pu kansky's condition, then the representations pi(i) = ind(Hi)G chi(f) [ i = 1, 2, H(i) = exp h(i), chi(f) (exp X) = e(if)(X) for X in g], are irreducible and equivalent. The main problem for constructing an inter twining operator is to prove the convergence of a certain integral. In this Note we present an explicit intertwining operator for pi1 and pi 2 which avoids this difficulty.