By Langlands duality one usually understands a correspondence between automorphic representations of a reductive group G over the ring of adels of a field F , and homomorphisms from the Galois group Gal(F/F ) to the Langlands dual group GL. It was originally introduced in the case when F is a number field or the field of rational functions on a curve over a finite field [1]. Recently A. Beilins...

This paper begins the project of adapting the 1992 book by Adams, Barbasch and Vogan on the Langlands classification of admissible representations of real groups, to padic groups, continuing in the direction charted by Vogan in his 1993 paper on the Langlands correspondence. This paper presents three theorems in that direction. The first theorem shows how Lusztig’s work on perverse sheaves aris...

We state a conjecture that relates the derived category of smooth representations $p$ -adic split reductive group with (quasi-)coherent sheaves on stack L-parameters. investigate in case principal block ${\rm GL}_n$ by showing functor should be given tensor product family interpolating modified Langlands correspondence over L-parameters is suggested work Helm and Emerton Helm.

We construct analogues of the Hecke operators for moduli space G-bundles on a curve X over local field F with parabolic structures at finitely many points. conjecture that they define commuting compact normal Hilbert half-densities this space. In case F=C, we also their joint spectrum is in natural bijection set LG-opers real monodromy. This may be viewed as an analytic version Langlands corres...