Harish-Chandra character formula

E250730
mathematical theorem result in representation theory

The Harish-Chandra character formula is a fundamental result in representation theory that gives an explicit expression for the characters of irreducible admissible representations of real reductive Lie groups.

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All labels observed (4)

Label Occurrences
Harish-Chandra character formula canonical 3
Harish-Chandra characters 1
Harish-Chandra theory of representations 1

Statements (45)

Predicate Object
instanceOf mathematical theorem ⓘ
result in representation theory ⓘ
appearsIn Harish-Chandra character formula self-linksurface differs ⓘ
surface form: Harish-Chandra’s collected papers on harmonic analysis
appliesTo irreducible admissible representations ⓘ
real reductive Lie groups ⓘ
assumes admissibility of representation ⓘ
reductivity of the Lie group ⓘ
codomain distributions on the group ⓘ
concerns behavior of characters on regular semisimple set ⓘ
trace of representation operators ⓘ
context harmonic analysis on real reductive groups ⓘ
unitary representation theory of semisimple Lie groups ⓘ
describes characters of irreducible admissible representations ⓘ
domain Lie algebra of a real reductive Lie group ⓘ
field Lie theory ⓘ
harmonic analysis ⓘ
representation theory ⓘ
formalism distribution characters on real reductive Lie groups ⓘ
generalizes Weyl character formula ⓘ
gives explicit expression for characters ⓘ
hasComponent denominator involving roots ⓘ
numerator involving highest weight data ⓘ
sum over Weyl group elements ⓘ
historicalPeriod 20th century mathematics ⓘ
influenced modern representation theory of real groups ⓘ
theory of automorphic representations ⓘ
involves conjugacy classes ⓘ
distribution characters ⓘ
orbital integrals ⓘ
regular semisimple elements ⓘ
namedAfter Harish-Chandra ⓘ
provedBy Harish-Chandra ⓘ
relatedTo Langlands classification ⓘ
Plancherel theorem for real reductive groups ⓘ
surface form: Plancherel formula for real reductive groups

discrete series representations ⓘ
tempered representations ⓘ
typeOf character formula ⓘ
usedFor classification of irreducible admissible representations ⓘ
computation of characters ⓘ
harmonic analysis on semisimple Lie groups ⓘ
uses Cartan subalgebras ⓘ
surface form: Cartan subalgebra

Harish-Chandra isomorphism ⓘ
Harish-Chandra regularity theorem ⓘ
Weyl group ⓘ
root system ⓘ

Referenced by (6)

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

Harish-Chandra → notableWork → Harish-Chandra character formula ⓘ
Weyl character formula → relatedTo → Harish-Chandra character formula ⓘ
Cartan subalgebras → usedFor → Harish-Chandra character formula ⓘ
this entity surface form: Harish-Chandra theory of representations
Harish → notableFor → Harish-Chandra character formula ⓘ
subject surface form: Harish-Chandra
Harish-Chandra character formula → appearsIn → Harish-Chandra character formula self-linksurface differs ⓘ
this entity surface form: Harish-Chandra’s collected papers on harmonic analysis
Plancherel theorem for real reductive groups → involves → Harish-Chandra character formula ⓘ
this entity surface form: Harish-Chandra characters