On intertwining operators for \(GL_ N(F)\), F a nonarchimedean local field
Let F be a nonarchimedean local field of residual characteristic p. As a first step toward a construction of the set of irreducible supercuspidal representations of \(GL_ N(F)\) when \(p| N\), the authors generalize a theorem of Howe to the wildly ramified case. More precisely let E be a finite-dimensional extension of F, let V be a finite-dimensional vector space over E and let \(\alpha\) be a primitive element of E/F with ``good arithmetic properties''. The main result asserts, roughly speaking, that the g in \(GL_ F(V)\) such that \(g\alpha g^{-1}=\alpha\) up to ``small terms'' lie in \(GL_ E(V)\) up to equally small terms. The paper is rather difficult to read because of its technical nature and of its numerous notations.
irreducible supercuspidal representations
scientific article; zbMATH DE number 4087937
scientific article