Representation Theory and Automorphic Functions
E270392
"Representation Theory and Automorphic Functions" is a seminal mathematical work by Israel Gelfand that develops the connections between representation theory of groups and the theory of automorphic forms, with deep applications in number theory and harmonic analysis.
All labels observed (1)
| Label | Occurrences |
|---|---|
| Representation Theory and Automorphic Functions canonical | 1 |
How this entity was disambiguated
This entity first appeared as the object of triple T2475547 — 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: Representation Theory and Automorphic Functions Context triple: [Israel Gelfand, notableWork, Representation Theory and Automorphic Functions]
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A.
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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B.
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.
-
C.
Deligne–Lusztig theory
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.
-
D.
Plancherel theorem for real reductive groups
The Plancherel theorem for real reductive groups is a fundamental result in representation theory that describes how square-integrable functions on a real reductive Lie group decompose into irreducible unitary representations, generalizing Fourier analysis to this non-abelian setting.
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E.
Harish-Chandra isomorphism
The Harish-Chandra isomorphism is a fundamental result in representation theory that identifies the center of the universal enveloping algebra of a semisimple Lie algebra with the algebra of Weyl group–invariant polynomials on a Cartan subalgebra.
- 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: Representation Theory and Automorphic Functions Target entity description: "Representation Theory and Automorphic Functions" is a seminal mathematical work by Israel Gelfand that develops the connections between representation theory of groups and the theory of automorphic forms, with deep applications in number theory and harmonic analysis.
-
A.
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.
-
B.
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.
-
C.
Deligne–Lusztig theory
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.
-
D.
Plancherel theorem for real reductive groups
The Plancherel theorem for real reductive groups is a fundamental result in representation theory that describes how square-integrable functions on a real reductive Lie group decompose into irreducible unitary representations, generalizing Fourier analysis to this non-abelian setting.
-
E.
Harish-Chandra isomorphism
The Harish-Chandra isomorphism is a fundamental result in representation theory that identifies the center of the universal enveloping algebra of a semisimple Lie algebra with the algebra of Weyl group–invariant polynomials on a Cartan subalgebra.
- F. None of above. chosen
Statements (44)
| Predicate | Object |
|---|---|
| instanceOf |
mathematics book
ⓘ
monograph ⓘ |
| author |
Israel Gelfand
ⓘ
surface form:
I. M. Gelfand
Israel Gelfand ⓘ |
| authorAffiliation | Moscow State University ⓘ |
| contribution |
applies representation theory to the study of automorphic functions
ⓘ
develops connections between representation theory and automorphic forms ⓘ influenced the development of the Langlands program ⓘ |
| era | 20th-century mathematics ⓘ |
| field |
automorphic forms
ⓘ
harmonic analysis ⓘ number theory ⓘ representation theory ⓘ |
| hasApplication |
automorphic representations
ⓘ
harmonic analysis ⓘ number theory ⓘ |
| language | Russian ⓘ |
| mathematicalDiscipline | pure mathematics ⓘ |
| notableFor |
impact on modern number theory
ⓘ
impact on the theory of unitary representations ⓘ systematic use of representation theory in automorphic form theory ⓘ |
| relatedTo |
Langlands program
ⓘ
automorphic representations ⓘ modular forms on the upper half-plane ⓘ representation theory of GL(2) ⓘ representation theory of SL(2,R) ⓘ |
| subjectOf |
research in automorphic forms
ⓘ
research in representation theory ⓘ |
| topic |
Eisenstein series
ⓘ
Fourier analysis on groups ⓘ Hecke operators ⓘ L-functions ⓘ adelic methods in number theory ⓘ automorphic functions ⓘ discrete series representations ⓘ harmonic analysis on groups ⓘ modular forms ⓘ non-abelian harmonic analysis ⓘ principal series representations ⓘ representation theory of reductive groups ⓘ representation theory of semisimple Lie groups ⓘ representations of Lie groups ⓘ spectral decomposition ⓘ unitary representations of groups ⓘ |
How these facts were elicited
The pipeline generated the facts above by prompting gpt-5.1 with this entity's name + description and the instruction below.
Instruction
You are a knowledge base construction expert. Given a subject entity and a description of it, return factual statements that you know for the subject as a JSON list of dictionaries(triples), where keys must be "subject", "predicate" and "object". The number of facts may be very high, between 25 to 50 or more, for very popular subjects. For less popular subjects, the number of facts can be very low, like 5 or 10. # Requirements - If you don't know the subject at all, return an empty list. - If the subject is not a named entity, return an empty list. - Include at least one triple where predicate is "instanceOf". - Do not get too wordy. - Separate several objects into multiple triples with one object.
Input
Subject: Representation Theory and Automorphic Functions Description of subject: "Representation Theory and Automorphic Functions" is a seminal mathematical work by Israel Gelfand that develops the connections between representation theory of groups and the theory of automorphic forms, with deep applications in number theory and harmonic analysis.
Referenced by (1)
Full triples — surface form annotated when it differs from this entity's canonical label.