Introduction 1 1. The unramified global Langlands correspondence 5 2. Classical local Langlands correspondence 9 3. Geometric local Langlands correspondence over C 12 4. Center and opers 18 5. Opers vs. local systems 23 6. Harish–Chandra categories 26 7. Local Langlands correspondence: unramified case 30 8. Local Langlands correspondence: tamely ramified case 41 9. Ramified global Langlands cor...

We describe in brief some aspects of the Langlands program, focussing on Euler products, and also some new constructions, where Euler products are replaced by twisted Euler products. The twisted Euler products are related to automorphic forms on metaplectic groups. 2000 Mathematics Subject Classification: 11F66, 11F55, 11F70, 11M41, 22E55.

In this paper, we take some initial steps towards illuminating the (hypothetical) p-adic local Langlands functoriality principle relating Galois representations of a p-adic field L and admissible unitary Banach space representations of G(L) when G is a split reductive group over L. 2000 Mathematics Subject Classification: 11F80, 11S37, 22E50

We show that the p-adic Galois representations attached to Hilbert modular forms of motivic weight are potentially semistable at all places above p and are compatible with the local Langlands correspondence at these places, proving this for those forms not covered by the previous works of T. Saito and of D. Blasius and J. Rogawski. 2000 Mathematics Subject Classification: 11F80, 11F41

This article is an introduction to the early life and work of Robert P. Langlands, creator and founder of the Langlands program. The story is, to a large extent, told by Langlands himself, in his own words. Our focus is on two of Langlands’ major discoveries: automorphic L-functions and the principle of functoriality. It was Langlands’ desire to communicate his excitement about his newly discov...

This paper is concerned with representations of split orthogonal and quasi-split unitary groups over a nonarchimedean local field which are not generic, but which support a unique model of a different kind, the generalized Bessel model. The properties of the Bessel models under induction are studied, and an analogue of Rodier’s theorem concerning the induction of Whittaker models is proved for ...

The local Langlands correspondence for GL(n) of a non-Archimedean local field F parametrizes irreducible admissible representations of GL(n, F ) in terms of representations of the Weil-Deligne group WDF of F . The correspondence, whose existence for p-adic fields was proved in joint work of the author with R. Taylor, and then more simply by G. Henniart, is characterized by its preservation of s...

We have determined composition series of a class induced representations appearing in Mœglin–Tadić classification discrete series. The result is further used to determine the certain from Langlands quotients. This should provide more information on decomposing standard as well Jacquet modules series, which has applications automorphic forms.

Using theta correspondence, we obtain a classification of irreducible representations an arbitrary even orthogonal group (i.e. the local Langlands correspondence) by deducing it from correspondence for symplectic groups due to Arthur. Moreover,we show that our classifications coincide with established Arthur and formulated precisely Atobe-Gan quasi-split groups.