Some properties of covering pairs
Let \(F\) be a non-archimedean local field and let \(G\) be the group of \(F\)-points of a connected reductive algebraic group over \(F\). The present article contributes to the theory of smooth representations of \(G\) over a field \(R\) of characteristic different from the residual characteristic of \(F\). Let \(M\) be a Levi subgroup of \(G\). Given a pair \((J_M,\tau_M)\) consisting of an open compact subgroup \(J_M\) of \(M\) and an irreducible smooth representation \(\tau_M\) of \(J_M\) over \(R\), we have the notion of covering pair (or \(G\)-cover) of \((J_M,\tau_M)\), introduced by Bushnell and Kutzko for \(R = {\mathbb C}\) and generalized by M.-F. Vignéras. The results proved in the paper concern maximality of a covering pair, the characterization of covering pairs by certain properties and their relation to parabolic induction. Also M.-F. Vignéras' result is included that all irreducible smooth representations of \(G\) over \(R\) are admissible and that all simple Hecke modules are finite-dimensional.
scientific article; zbMATH DE number 2156220