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On intertwining operators for \(GL_ N(F)\), F a nonarchimedean local field. (English) Zbl 0665.22006

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.
Reviewer: G.Christol

MSC:

22E50 Representations of Lie and linear algebraic groups over local fields
11S15 Ramification and extension theory
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