Whittaker models and the integral Bernstein center for GL_n

Abstract

We establish integral analogues of results of Bushnell and Henniart for spaces of Whittaker functions arising from the groups GL_n(F) for F a p-adic field. We apply the resulting theory to the existence of representations arising from the conjectural "local Langlands correspondence in families" of Emerton-Helm, and reduce the question of the existence of such representations to a natural conjecture relating the integral Bernstein center of GL_n(F) to the deformation theory of Galois representations.

17 pages

References in corpus (2)

• Représentations lisses modulo l de GL(m,D)
• The Bernstein center of the category of smooth $W(k)[G{L}_n(F)]$-modules

Cited by in corpus (11)

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• Families of Canonical Local Periods on Spherical Varieties
• The local Langlands correspondence in families and Ihara's lemma for U(n)
• Functorial Zeta Integrals
• On the local converse theorem and the descent theorem in families
• Characterizing the mod-$\ell$ local Langlands correspondence by nilpotent gamma factors
• The universal unramified module for GL(n) and the Ihara conjecture