We carry out the first nontrivial cases of the limiting process proposed by Langlands in his manuscript Beyond Endoscopy, with technical variations that enable us to treat the limit unconditionally. This gives an elementary proof, on GL(2), of the classification of forms such that the symmetric square L-function has a pole (including, implicitly, the construction of these forms). The result of ...

Inside the universal deformation space of a local Galois representation one has the set of deformations which are potentially semi-stable of given p-adic Hodge and Galois type. It turns out these points cut out a closed subspace of the deformation space. A deep conjecture due to Breuil-Mézard predicts that part of the structure of this space can be described in terms of the local Langlands corr...

Article history: Received 15 August 2010 Revised 31 December 2010 Accepted 3 January 2011 Available online xxxx Communicated by David Goss MSC: primary 11G18, 11G09 secondary 14H40

Let $G$ be a reductive $p$-adic group‎. ‎We consider the general question‎ ‎of whether the reducibility of an induced representation can be detected in a‎ ‎``co-rank one‎" ‎situation‎. ‎For smooth complex representations induced from supercuspidal‎ ‎representations‎, ‎we show that a sufficient condition is the existence of a subquotient‎ ‎that does not appear as a subrepresentation‎. ‎An import...

‎We study $R$-groups for $p$-adic inner forms of quasi-split special unitary groups‎. ‎We prove Arthur's conjecture‎, ‎the isomorphism between the Knapp-Stein $R$-group and the Langlands-Arthur $R$-group‎, ‎for quasi-split special unitary groups and their inner forms‎. ‎Furthermore‎, ‎we investigate the invariance of the Knapp-Stein $R$-group within $L$-packets and between inner forms‎. ‎This w...