Deligne–Lusztig theory

E269188

mathematical theory representation theory framework

Deligne–Lusztig theory is a framework in algebraic geometry and representation theory that constructs and studies representations of finite groups of Lie type using varieties defined over finite fields.

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All labels observed (2)

Label	Occurrences
Deligne–Lusztig theory canonical	1
Deligne–Lusztig varieties	1

Statements (47)

Predicate	Object
instanceOf	mathematical theory ⓘ representation theory framework ⓘ
appliesTo	finite groups of Lie type ⓘ
basedOn	Deligne–Lusztig theory self-linksurface differs ⓘ surface form: Deligne–Lusztig varieties cohomology of algebraic varieties ⓘ
constructs	character sheaves precursors ⓘ cuspidal representations ⓘ representations of finite groups of Lie type ⓘ unipotent representations ⓘ virtual representations ⓘ
contextOf	Chevalley groups ⓘ finite groups of Lie type classification ⓘ reductive groups over finite fields ⓘ
describedIn	"Representations of reductive groups over finite fields" ⓘ
field	algebraic geometry ⓘ representation theory ⓘ
generalizes	classical character theory of finite groups ⓘ
influenced	Lusztig’s theory of character sheaves ⓘ geometric representation theory ⓘ modern approaches to the Langlands correspondence ⓘ
introducedBy	George Lusztig ⓘ Pierre Deligne ⓘ
involves	Borel subalgebras ⓘ surface form: Borel subgroups Bruhat decomposition ⓘ Weyl group ⓘ surface form: Weyl groups maximal tori in reductive groups ⓘ
provides	geometric construction of representations ⓘ geometric interpretation of character values ⓘ parameterization of irreducible representations ⓘ
publishedIn	Annals of Mathematics ⓘ
relatesTo	Bruhat–Tits theory ⓘ Langlands program ⓘ Springer correspondence ⓘ Tits building ⓘ character sheaves ⓘ modular representation theory ⓘ
studies	Green functions ⓘ Hecke algebra ⓘ surface form: Hecke algebras characters of finite groups of Lie type ⓘ unipotent characters ⓘ
uses	Frobenius endomorphism ⓘ Weil conjectures techniques ⓘ algebraic groups over finite fields ⓘ varieties over finite fields ⓘ étale cohomology ⓘ ℓ-adic cohomology ⓘ
yearIntroduced	1976 ⓘ

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Input

Subject: Deligne–Lusztig theory
Description of subject: Deligne–Lusztig theory is a framework in algebraic geometry and representation theory that constructs and studies representations of finite groups of Lie type using varieties defined over finite fields.

Referenced by (2)

Full triples — surface form annotated when it differs from this entity's canonical label.

Pierre Deligne → knownFor → Deligne–Lusztig theory ⓘ

Deligne–Lusztig theory → basedOn → Deligne–Lusztig theory self-linksurface differs ⓘ

this entity surface form: Deligne–Lusztig varieties