Statements (23)
| Predicate | Object |
|---|---|
| gptkbp:instanceOf |
gptkb:mathematical_concept
|
| gptkbp:category |
algebraic groups
duality |
| gptkbp:defines |
The Langlands dual group of a connected reductive algebraic group G is a complex reductive group whose root datum is dual to that of G.
|
| gptkbp:example |
The Langlands dual of GL(n) is GL(n).
The Langlands dual of SL(n) is PGL(n). The Langlands dual of SO(2n+1) is Sp(2n). The Langlands dual of Sp(2n) is SO(2n+1). |
| gptkbp:field |
gptkb:algebraic_geometry
gptkb:mathematics number theory representation theory |
| https://www.w3.org/2000/01/rdf-schema#label |
Langlands dual group
|
| gptkbp:introduced |
gptkb:Robert_Langlands
|
| gptkbp:property |
The weight lattice and coweight lattice are interchanged in the dual group.
The root system of the Langlands dual group is dual to the root system of the original group. |
| gptkbp:relatedTo |
gptkb:Langlands_program
reductive algebraic group |
| gptkbp:usedIn |
automorphic forms
Galois representations reciprocity laws |
| gptkbp:bfsParent |
gptkb:Robert_Langlands
|
| gptkbp:bfsLayer |
4
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