Weil’s "Sur certains groupes d’opérateurs unitaires"
E860127
Weil’s "Sur certains groupes d’opérateurs unitaires" is a foundational mathematical paper by André Weil that introduces and studies the Weil representation, a key construction in representation theory and number theory.
All labels observed (1)
| Label | Occurrences |
|---|---|
| Weil’s "Sur certains groupes d’opérateurs unitaires" canonical | 1 |
How this entity was disambiguated
This entity first appeared as the object of triple T10389333 — 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: Weil’s "Sur certains groupes d’opérateurs unitaires" Context triple: [Weil representation, appearsIn, Weil’s "Sur certains groupes d’opérateurs unitaires"]
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A.
Stone’s theorem on one-parameter unitary groups
Stone’s theorem on one-parameter unitary groups is a fundamental result in functional analysis and quantum mechanics that characterizes strongly continuous one-parameter unitary groups as being generated by unique self-adjoint operators.
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B.
Hilbert–Schmidt operators
Hilbert–Schmidt operators are a class of compact operators on Hilbert spaces characterized by having finite Hilbert–Schmidt norm, playing a central role in functional analysis and operator theory.
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C.
L’intégration dans les groupes topologiques et ses applications
L’intégration dans les groupes topologiques et ses applications is a foundational mathematical monograph by André Weil that develops the theory of integration on topological groups and explores its far-reaching applications in analysis and number theory.
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D.
Theory of Linear Operations
Theory of Linear Operations is a foundational 1932 monograph by Stefan Banach that systematically developed functional analysis and the theory of Banach spaces.
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E.
Leçons d’analyse fonctionnelle
Leçons d’analyse fonctionnelle is a foundational textbook in functional analysis that helped shape the modern theory of linear operators and Banach and Hilbert spaces.
- 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: Weil’s "Sur certains groupes d’opérateurs unitaires" Target entity description: Weil’s "Sur certains groupes d’opérateurs unitaires" is a foundational mathematical paper by André Weil that introduces and studies the Weil representation, a key construction in representation theory and number theory.
-
A.
Stone’s theorem on one-parameter unitary groups
Stone’s theorem on one-parameter unitary groups is a fundamental result in functional analysis and quantum mechanics that characterizes strongly continuous one-parameter unitary groups as being generated by unique self-adjoint operators.
-
B.
Hilbert–Schmidt operators
Hilbert–Schmidt operators are a class of compact operators on Hilbert spaces characterized by having finite Hilbert–Schmidt norm, playing a central role in functional analysis and operator theory.
-
C.
L’intégration dans les groupes topologiques et ses applications
L’intégration dans les groupes topologiques et ses applications is a foundational mathematical monograph by André Weil that develops the theory of integration on topological groups and explores its far-reaching applications in analysis and number theory.
-
D.
Theory of Linear Operations
Theory of Linear Operations is a foundational 1932 monograph by Stefan Banach that systematically developed functional analysis and the theory of Banach spaces.
-
E.
Leçons d’analyse fonctionnelle
Leçons d’analyse fonctionnelle is a foundational textbook in functional analysis that helped shape the modern theory of linear operators and Banach and Hilbert spaces.
- F. None of above. chosen
Statements (49)
| Predicate | Object |
|---|---|
| instanceOf |
mathematical paper
ⓘ
research article ⓘ |
| author |
André Weil
NERFINISHED
ⓘ
Weil, André NERFINISHED ⓘ |
| citedAs | Weil, Sur certains groupes d’opérateurs unitaires NERFINISHED ⓘ |
| citedFor |
applications to theta functions
ⓘ
construction of the metaplectic group ⓘ introduction of the Weil representation ⓘ |
| context |
complex local fields
ⓘ
local fields ⓘ p-adic fields ⓘ real local fields ⓘ |
| field |
algebraic number theory
ⓘ
automorphic forms ⓘ harmonic analysis on groups ⓘ mathematics ⓘ pure mathematics ⓘ representation theory ⓘ |
| hasInfluenceOn |
Langlands program
NERFINISHED
ⓘ
modern representation theory of reductive groups ⓘ theory of automorphic representations ⓘ theta correspondence ⓘ |
| introducesConcept |
Weil representation
NERFINISHED
ⓘ
metaplectic representation ⓘ |
| isFoundationalFor |
Weil representation theory
ⓘ
metaplectic group theory ⓘ theta correspondence in automorphic forms ⓘ |
| keyConstruction |
Weil representation of the metaplectic group
NERFINISHED
ⓘ
oscillator representation ⓘ |
| language | French ⓘ |
| mainTopic |
Heisenberg group
NERFINISHED
ⓘ
Weil representation NERFINISHED ⓘ harmonic analysis ⓘ metaplectic group NERFINISHED ⓘ number theory ⓘ representation theory ⓘ symplectic group ⓘ theta functions ⓘ unitary representations ⓘ |
| mathematicianSubject | André Weil NERFINISHED ⓘ |
| relatedTo |
Fourier transform on local fields
NERFINISHED
ⓘ
Stone–von Neumann theorem NERFINISHED ⓘ quadratic forms ⓘ symplectic vector spaces ⓘ theta series ⓘ |
| studies |
Heisenberg group representations
ⓘ
intertwining operators ⓘ projective representations of the symplectic group ⓘ unitary representations of the symplectic group ⓘ |
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: Weil’s "Sur certains groupes d’opérateurs unitaires" Description of subject: Weil’s "Sur certains groupes d’opérateurs unitaires" is a foundational mathematical paper by André Weil that introduces and studies the Weil representation, a key construction in representation theory and number theory.
Referenced by (1)
Full triples — surface form annotated when it differs from this entity's canonical label.