a branch of mathematics, the Langlands dual LG of a reductive algebraic group G (also called the L-group of G) is a group that controls the representation...

mathematics, the dual group refer to: Pontryagin dual, of a locally compact abelian group Langlands dual, of a reductive algebraic group The dual group in the Deligne–Lusztig...

linear group GL(n), other connected reductive groups can be used. Furthermore, given such a group G, Langlands constructs the Langlands dual group LG, and...

homomorphisms of the Weil group of R or C into the Langlands dual group. g is the Lie algebra of a real reductive Lie group G in the Harish-Chandra class...

ingredients of the geometric Langlands correspondence. Their work shows that the Langlands correspondence is closely related to S-duality in quantum field theory...

Langlands dual Langlands group Langlands program Langlands, Queensland, a locality in the Western Downs Region, Queensland, Australia Langlands Park, a...

In mathematics, L-group or l-group may refer to the following groups: The Langlands dual, LG, of a reductive algebraic group G A group in L-theory, L(G)...

group G(k((t))) and which describes the representation theory of the Langlands dual group LG through what is known as the geometric Satake correspondence....

on Tamagawa numbers Langlands classification, Langlands dual group, Langlands program, geometric Langlands program Special group, essential dimension...

correspondence between representations of a reductive group and conjugacy classes of a Langlands dual group, and the unipotent representations should be roughly...

group G is simultaneously replaced by its Langlands dual group LG and n G {\displaystyle n_{G}} is an integer depending on the choice of gauge group....

bounding monodromy groups. The Geometric Satake equivalence establishes an equivalence between representations of the Langlands dual group L G {\displaystyle...

representation π of a reductive group G over a global field and a finite-dimensional complex representation r of the Langlands dual group LG of G, generalizing...

connected reductive algebraic group over the algebraically closed field K {\displaystyle K} , then its Langlands dual group L G {\displaystyle {}^{L}G}...

Phelan Langlands, CC FRS FRSC (/ˈlæŋləndz/; born October 6, 1936) is a Canadian mathematician. He is best known as the founder of the Langlands program...

the geometric Langlands correspondence relates algebraic geometry and representation theory. It is a reformulation of the Langlands correspondence obtained...

group G {\displaystyle G} to its Langlands dual group. This theory is also important in the context of the holographic principle. There is a duality between...

G {\displaystyle Gr_{G}} with representations of the Langlands dual group of a reductive group G - see Mirković & Vilonen (2007). A proof of the Weil...

the Langlands dual group (or L-group), except here the dual group is defined over a finite field rather than over the complex numbers. The dual group has...

Lagrange duality Langlands dual Lefschetz duality Local Tate duality Opposite category Poincaré duality Twisted Poincaré duality Poitou–Tate duality Pontryagin...

mathematics, the Langlands–Shahidi method provides the means to define automorphic L-functions in many cases that arise with connected reductive groups over a number...

In mathematics, the local Langlands conjectures, introduced by Robert Langlands (1967, 1970), are part of the Langlands program. They describe a correspondence...

Dual system Koszul duality Langlands dual Linear programming#Duality List of dualities Matlis duality Petrie duality Pontryagin duality S-duality T-duality...

In mathematics, the Langlands–Deligne local constant, also known as the local epsilon factor or local Artin root number (up to an elementary real function...

Robert Langlands and is called the Langlands classification. Let G be a locally compact totally disconnected group (such as a reductive algebraic group over...

to topological groups that are not commutative. Since locally compact abelian groups have a well-understood theory, Pontryagin duality, which includes...

of G make up its unitary dual. This set can be identified with the spectrum of the C*-algebra associated with G by the group C*-algebra construction....

409–451. (with Zhiwei Yun) "Integral homology of loop groups via Langlands dual groups", Representation Theory 15 (2011), 347–369. (with An Huang, Bong...

and in category theory in general, ∞ = ω. EGA FGA SGA Abstract Stone Duality nLab, just as a higher-dimensional Wikipedia, started in late 2008; see...

T-duality (short for target-space duality) in theoretical physics is an equivalence of two physical theories, which may be either quantum field theories...