Knapp-Wallach Szegő integrals. II. The higher parabolic rank case

Abstract

Let G G be a connected reductive linear Lie group with compact center and real rank l l . For each integer k ( 1 ⩽ k ⩽ l ) k(1 \leqslant k \leqslant l) and each discrete series representation π \pi of G G , an explicit embedding of π \pi into a generalized principal series representation induced from a parabolic subgroup of rank k k is given. The existence of such embeddings was proved by W. Schmid. In this paper an explicit integral formula with Szegö kernel is given which provides these mappings.