GADTs can be represented either as their Church encodings a la Atkey, or fixpoints Johann and Polonsky. While GADT its encoding need not support map function satisfying the functor laws, fixpoint representation of must such even to well-defined. The two representations thus same in general. This observation forces choice data types languages supporting GADTs. In this paper we show that choosing...

‎In The endoscopic classification of representations‎‎, ‎J‎. ‎Arthur has proved the Langlands' classification for discrete series of p-adic classical groups‎. ‎This uses endoscopy and twisted endoscopy‎. ‎In this very short note‎, ‎we remark that the normalization ‎$‎rm‎grave{a}‎$‎ la Langlands-Shahidi of the intertwining operators‎, ‎allows to avoid endoscopy‎. ‎This is based on the intertwini...

Ngô Bao Châu recently won a Fields Medal for his work on the Fundamental Lemma, conjectured by Langlands many years ago. But the relationship between the result proved by him and Langlands’ original conjecture might not be so clear to someone who has not followed the development closely. The original idea involvedwhat Langlands calls endoscopy—to explain harmonic analysis on reductive groups ov...

In this paper, we present a refinement of the global Langlands correspondence for discrete symplectic motives of rank 2n over Q. To such a motive Langlands conjecturally associates a generic, automorphic representation π of the split orthogonal group SO2n+1 over Q, which appears with multiplicity one in the cuspidal spectrum. Using the local theory of generic representations of odd orthogonal g...

In the late 1960s, Robert Langlands proposed a new and far-reaching connection between the representation theory of Lie groups over real and -adic fields, and the structure of the Galois groups of these fields [24]. Even though this local Langlands correspondence remains largely conjectural, the relation that it predicts between representation theory and number theory has profoundly changed our...