On the composition series of the standard Whittaker \((\mathfrak{g},K)\)-modules (Q2846988)

The aim of the article under review is to determine the composition series of suitable subspaces of Whittaker models, which the author calls the standard Whittaker \((\mathfrak{g} ,K)\)-modules. (Note that these modules are different from the ``standard Whittaker modules'' defined by \textit{B. Kostant} in [Invent. Math. 48, No. 2, 101--184 (1978; Zbl 0405.22013)]). To describe the \((\mathfrak{g} ,K)\)-modules, let \(G\) be a real reductive linear Lie group and \(G = KAN\) an Iwasawa decomposition. Given a unitary character \(\eta : N \to \mathbb{C}^\times\) of \(N\), let \(C^\infty(G/N;\eta)\) be the space of Whittaker functions on \(G\), namely, \(C^\infty(G/N;\eta) := \{ f \in C^\infty(G) \; :\; f(gn) = \eta(n)^{-1}f(g) \text{ for }g \in G\) and \(n \in N\)