Langlands conjecture

plural Langlands conjectures · alternative Langlands' conjecture

1. mathematicsAny of the conjectures that comprise the Langlands programme.

   It^([the Langlands functoriality conjecture]) is closely related to the local Langlands conjectures, which amount to a (conjectural) classification of the representations of reductive groups over local fields.

   1998, Daniel Bump, Automorphic Forms and Representations, Cambridge University Press, page 90

   2 more examples

   This abelian case of the Geometric Langlands Conjecture amounts to the well known result that any rank of one local system (or: line bundle with flat connection) on the curve C extends uniquely to J, and this extension is natural with respect to the Abel-Jacobi map.

   2009, Huai-Dong Cao, Shing-Tung Yau, editors, Surveys in Differential Geometry, International Press, page 86

   The Langlands conjectures predict the existence of a correspondence between the n-dimensional representations of #92;mathcal#123;G#125;#95;k and the automorphic representations of #92;mathrm#123;GL#125;#95;n(#92;mathbb#123;A#125;) which preserves these analytic invariants.

   2013, J. W. Cogdell, “10: Langlands Conjectures for GLₙ”, in Joseph Bernstein, Stephen Gelbart, editors, An Introduction to the Langlands Program, Springer, page 229