Whittaker models and the integral Bernstein center for \(\mathrm{GL}_n\)

DOI10.1215/00127094-3450422zbMath1343.11053arXiv1210.1789OpenAlexW1728684668MaRDI QIDQ726777

David Helm

Publication date: 14 July 2016

Published in: Duke Mathematical Journal (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1210.1789

zbMATH Keywords

local Langlands correspondenceWhittaker functionsBernstein center

Mathematics Subject Classification ID

Congruences for modular and (p)-adic modular forms (11F33) Representations of Lie and linear algebraic groups over local fields (22E50) Representation-theoretic methods; automorphic representations over local and global fields (11F70) Langlands-Weil conjectures, nonabelian class field theory (11S37)

Related Items (11)

The Kirillov model in families ⋮ Speculations on the mod \(p\) representation theory of \(p\)-adic groups ⋮ On the local converse theorem and the descent theorem in families ⋮ On the derived category of the Iwahori–Hecke algebra ⋮ Zeta morphisms for rank two universal deformations ⋮ Representations of \(p\)-adic groups over commutative rings ⋮ Curtis homomorphisms and the integral Bernstein center for \(\mathrm{GL}_n\) ⋮ Local Langlands correspondence, local factors, and zeta integrals in analytic families ⋮ Converse theorems and the local Langlands correspondence in families ⋮ CHARACTERIZING THE MOD- LOCAL LANGLANDS CORRESPONDENCE BY NILPOTENT GAMMA FACTORS ⋮ \(p\)-adic properties of motivic fundamental lines

Cites Work

• \(\ell\)-integral nonabelian Lubin-Tate theory
• A local-global compatibility conjecture in the \(p\)-adic Langlands programme for \(\text{GL}_{2}/\mathbb Q\)
• Automorphy for some \(l\)-adic lifts of automorphic mod \(l\) Galois representations. With Appendix A, summarizing unpublished work of Russ Mann, and Appendix B by Marie-France Vignéras.
• Conducteur des représentations du groupe linéaire
• The projective envelope of a cuspidal representation of a finite linear group
• The local Langlands correspondence for $GL_n$ in families
• The Admissible Dual of GL(N) via Compact Open Subgroups. (AM-129)
• Generalized Whittaker models and the Bernstein center
• THE BERNSTEIN CENTER OF THE CATEGORY OF SMOOTH -MODULES

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