Degenerate Principal Series Representations of GL_n(C) and GL_n(R)

摘要

Let F be the field C or R. For 1<=k<=[n/2], let P_k be the maximal parabolic subgroup of GL_n(F) with its Levi factor isomorphic to GL_(n-k)(F) X GL_k(F). In this paper, we explicitly calculate the action of the enveloping algebra of gl_n(F) on the degenerate principal series representations induced from characters of P_k. We address composition series, K-types and unitarity.