Essential Whittaker functions for \(\mathrm{GL}(n)\) (Q2437870)

In the paper under review, the author studies generic representations of the general linear group \(\mathrm{GL}(n, F)\), where \(F\) denotes a nonarchimedean local field, with a ring of integers \(\mathfrak{D}\). Let us denote by \(\pi\) an irreducible generic representation of \(\mathrm{GL}(n,F)\) and by \(\theta\) a non-degenerate character of the standard unipotent subgroup of \(\mathrm{GL}(n,F)\). Using restrictions of Whittaker functions and Bernstein-Zelevinsky derivatives, the author provides a constructive proof of the existence of the (unique \(\mathrm{GL}(n-1, \mathfrak{D})\)-invariant) essential Whittaker function \(W_{\pi}^{\text{ess}}\) in the Whittaker model \(W(\pi, \theta)\) of the representation \(\pi\) with respect to \(\theta\).