Langlands group
In mathematics, the Langlands group is a conjectural group LF attached to each local or global field F, that satisfies properties similar to those of the Weil group. It was given that name by Robert K
Fundamental lemma (Langlands program)
In the mathematical theory of automorphic forms, the fundamental lemma relates orbital integrals on a reductive group over a local field to stable orbital integrals on its endoscopic groups. It was co
Geometric Langlands correspondence
In mathematics, the geometric Langlands correspondence is a reformulation of the Langlands correspondence obtained by replacing the number fields appearing in the original number theoretic version by
L-packet
In the field of mathematics known as representation theory, an L-packet is a collection of (isomorphism classes of) irreducible representations of a reductive group over a local field, that are L-indi
Whittaker model
In representation theory, a branch of mathematics, the Whittaker model is a realization of a representation of a reductive algebraic group such as GL2 over a finite or local or global field on a space
Theta correspondence
In mathematics, the theta correspondence or Howe correspondence is a mathematical relation between representations of two groups of a reductive dual pair. The local theta correspondence relates irredu
Picard modular surface
In mathematics, a Picard modular surface, studied by Picard, is a complex surface constructed as a quotient of the unit ball in C2 by a Picard modular group.Picard modular surfaces are some of the sim
Automorphic Forms on GL(2)
Automorphic Forms on GL(2) is a mathematics book by H. Jacquet and Robert Langlands where they rewrite Erich Hecke's theory of modular forms in terms of the representation theory of GL(2) over local f
Langlands program
In representation theory and algebraic number theory, the Langlands program is a web of far-reaching and influential conjectures about connections between number theory and geometry. Proposed by Rober
Waldspurger formula
In representation theory of mathematics, the Waldspurger formula relates the special values of two L-functions of two related admissible irreducible representations. Let k be the base field, f be an a
Base change lifting
In mathematics, base change lifting is a method of constructing new automorphic forms from old ones, that corresponds in Langlands philosophy to the operation of restricting a representation of a Galo
Gan–Gross–Prasad conjecture
In mathematics, the Gan–Gross–Prasad conjecture is a restriction problem in the representation theory of real or p-adic Lie groups posed by Gan Wee Teck, Benedict Gross, and Dipendra Prasad. The probl
Local Langlands conjectures
In mathematics, the local Langlands conjectures, introduced by Robert Langlands , are part of the Langlands program. They describe a correspondence between the complex representations of a reductive a
Endoscopic group
In mathematics, endoscopic groups of reductive algebraic groups were introduced by Robert Langlands in his work on the stable trace formula. Roughly speaking, an endoscopic group H of G is a quasi-spl
Taniyama group
In mathematics, the Taniyama group is a group that is an extension of the absolute Galois group of the rationals by the Serre group. It was introduced by Langlands using an observation by Deligne, and
Automorphic L-function
In mathematics, an automorphic L-function is a function L(s,π,r) of a complex variable s, associated to an automorphic representation π of a reductive group G over a global field and a finite-dimensio
Lafforgue's theorem
In mathematics, Lafforgue's theorem, due to Laurent Lafforgue, completes the Langlands program for general linear groups over algebraic function fields, by giving a correspondence between automorphic
Serre group
In mathematics, the Serre group S is the pro-algebraic group whose representations correspond to CM-motives over the algebraic closure of the rationals, or to polarizable rational Hodge structures wit
Kirillov model
In mathematics, the Kirillov model, studied by Kirillov, is a realization of a representation of GL2 over a local field on a space of functions on the local field. If G is the algebraic group GL2 and