Harish-Chandra character formula
E250730
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.
All labels observed (4)
| Label | Occurrences |
|---|---|
| Harish-Chandra character formula canonical | 3 |
| Harish-Chandra characters | 1 |
| Harish-Chandra theory of representations | 1 |
| Harish-Chandra’s collected papers on harmonic analysis | 1 |
How this entity was disambiguated
This entity first appeared as the object of triple T2267715 — resolving that mention is where its identity was fixed. The disambiguator weighed these candidate entities and picked the highlighted one (or “None”, minting a new entity). This is how homonymy is resolved: the same surface form can point to different entities.
NED1
Entity disambiguation (via context triple)
gpt-5-mini-2025-08-07
Target entity: Harish-Chandra character formula Context triple: [Harish-Chandra, notableWork, Harish-Chandra character formula]
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A.
Weyl character formula
The Weyl character formula is a fundamental result in representation theory that gives an explicit expression for the characters of irreducible finite-dimensional representations of semisimple Lie algebras and Lie groups.
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B.
Weil representation
The Weil representation is a fundamental projective unitary representation of symplectic groups (or their metaplectic covers) on spaces of functions, central to number theory, automorphic forms, and the theory of theta functions.
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C.
The Classical Groups: Their Invariants and Representations
The Classical Groups: Their Invariants and Representations is a foundational mathematical monograph by Hermann Weyl that systematically develops the theory of classical Lie groups, their invariants, and their representation theory.
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D.
Harish-Chandra
Harish-Chandra was a pioneering mathematician and physicist best known for his fundamental contributions to representation theory and harmonic analysis on Lie groups.
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E.
Selberg trace formula
The Selberg trace formula is a fundamental result in analytic number theory and spectral theory that relates lengths of closed geodesics on a Riemannian manifold to the spectrum of its Laplace operator, serving as a non-abelian analogue of the Poisson summation formula.
- F. None of above. chosen
- G. Unsure - the case is ambiguous/there is not enough information to decide.
NED2
Entity disambiguation (via description)
gpt-5-mini-2025-08-07
Target entity: Harish-Chandra character formula Target entity description: 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.
-
A.
Weyl character formula
The Weyl character formula is a fundamental result in representation theory that gives an explicit expression for the characters of irreducible finite-dimensional representations of semisimple Lie algebras and Lie groups.
-
B.
Weil representation
The Weil representation is a fundamental projective unitary representation of symplectic groups (or their metaplectic covers) on spaces of functions, central to number theory, automorphic forms, and the theory of theta functions.
-
C.
The Classical Groups: Their Invariants and Representations
The Classical Groups: Their Invariants and Representations is a foundational mathematical monograph by Hermann Weyl that systematically develops the theory of classical Lie groups, their invariants, and their representation theory.
-
D.
Harish-Chandra
Harish-Chandra was a pioneering mathematician and physicist best known for his fundamental contributions to representation theory and harmonic analysis on Lie groups.
-
E.
Selberg trace formula
The Selberg trace formula is a fundamental result in analytic number theory and spectral theory that relates lengths of closed geodesics on a Riemannian manifold to the spectrum of its Laplace operator, serving as a non-abelian analogue of the Poisson summation formula.
- F. None of above. chosen
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 ⓘ |
How these facts were elicited
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Input
Subject: Harish-Chandra character formula Description of subject: 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.
Referenced by (6)
Full triples — surface form annotated when it differs from this entity's canonical label.
this entity surface form:
Harish-Chandra theory of representations
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
this entity surface form:
Harish-Chandra characters