Triple
T12095298
| Position | Surface form | Disambiguated ID | Type / Status |
|---|---|---|---|
| Subject | Jacques Dixmier |
E288055
|
entity |
| Predicate | knownFor |
P22
|
FINISHED |
| Object |
Dixmier mapping in representation theory
The Dixmier mapping in representation theory is a correspondence introduced by Jacques Dixmier that relates primitive ideals in the universal enveloping algebra of a Lie algebra to coadjoint orbits, playing a key role in understanding the orbit method and the structure of representations.
|
E962402
|
NE FINISHED |
How this triple was built (4 steps)
Every LLM step that produced this triple, in pipeline order — named-entity classification, the disambiguation choices (the exact options shown, with the pick highlighted), and the generated description. The batch + timestamp of each is in the Provenance table below.
NER
Named-entity recognition
gpt-5-mini
Instruction
Given a phrase, classify it is english named entity (e.g., persons, organizations, works of art) in Latin script, or not (e.g., literals, dates, URLs, verbose phrases). For disambiguation, the statement where the phrase occurs as object is also given. Please return a JSON object with `phrase` (string, the phrase being analyzed) and `is_ne` (boolean, indicating whether the phrase is a Named Entity).
Input
Phrase: Dixmier mapping in representation theory | Statement: [Jacques Dixmier, knownFor, Dixmier mapping in representation theory]
NED1
Entity disambiguation (via context triple)
gpt-5-mini-2025-08-07
Target entity: Dixmier mapping in representation theory Context triple: [Jacques Dixmier, knownFor, Dixmier mapping in representation theory]
-
A.
Methods of Representation Theory
Methods of Representation Theory is a foundational multi-volume work in mathematics that systematically develops the theory of group and algebra representations, coauthored by Israel Gelfand and collaborators.
-
B.
Bernstein center in representation theory
The Bernstein center in representation theory is a commutative algebra that acts as the center of the category of smooth representations of a p-adic reductive group, playing a key role in decomposing and classifying these representations.
-
C.
Schur–Weyl duality
Schur–Weyl duality is a fundamental result in representation theory that links representations of the symmetric group and the general linear group via their commuting actions on tensor powers of a vector space.
-
D.
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.
-
E.
Representation Theory and Automorphic Functions
"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.
- F. None of above. chosen
- G. Unsure - the case is ambiguous/there is not enough information to decide.
NEDg
Description generation
gpt-5.1
Instruction
Generate a one-sentence description of the target entity. You are given a context triple in the form (subject, predicate, object), where the object is the target entity. # Instructions Use the triple to infer relevant information about the entity. Describe the entity based on what is most defining, well-known. Avoid repeating the information from the triple, unless really essential. # Response Format Return only the sentence: "Description: [one-sentence description of the target entity]"
Input
Entity: Dixmier mapping in representation theory Triple: [Jacques Dixmier, knownFor, Dixmier mapping in representation theory]
Generated description
The Dixmier mapping in representation theory is a correspondence introduced by Jacques Dixmier that relates primitive ideals in the universal enveloping algebra of a Lie algebra to coadjoint orbits, playing a key role in understanding the orbit method and the structure of representations.
NED2
Entity disambiguation (via description)
gpt-5-mini-2025-08-07
Target entity: Dixmier mapping in representation theory Target entity description: The Dixmier mapping in representation theory is a correspondence introduced by Jacques Dixmier that relates primitive ideals in the universal enveloping algebra of a Lie algebra to coadjoint orbits, playing a key role in understanding the orbit method and the structure of representations.
-
A.
Methods of Representation Theory
Methods of Representation Theory is a foundational multi-volume work in mathematics that systematically develops the theory of group and algebra representations, coauthored by Israel Gelfand and collaborators.
-
B.
Bernstein center in representation theory
The Bernstein center in representation theory is a commutative algebra that acts as the center of the category of smooth representations of a p-adic reductive group, playing a key role in decomposing and classifying these representations.
-
C.
Schur–Weyl duality
Schur–Weyl duality is a fundamental result in representation theory that links representations of the symmetric group and the general linear group via their commuting actions on tensor powers of a vector space.
-
D.
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.
-
E.
Representation Theory and Automorphic Functions
"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.
- F. None of above. chosen
Provenance (5 batches)
The batch behind each pipeline step, in order, with when it ran. Timestamps are batch-level — stages were processed in waves, so the object chain (NER → NED1 → NEDg → NED2) reads in order, but predicate / elicitation batches can sit in a different wave.
| Step | Stage | Batch ID | Status | When |
|---|---|---|---|---|
| creating | Elicitation | batch_69d6ab4964708190850585628b287b0c |
completed | April 8, 2026, 7:23 p.m. |
| NER | Named-entity recognition | batch_69d91550ce508190babf5755e1553734 |
completed | April 10, 2026, 3:20 p.m. |
| NED1 | Entity disambiguation (via context triple) | batch_69f5f66edf7881908f29b5b40b9d020f |
completed | May 2, 2026, 1:04 p.m. |
| NEDg | Description generation | batch_69f5fd7a9aa4819099af0f31c1fb9aab |
completed | May 2, 2026, 1:34 p.m. |
| NED2 | Entity disambiguation (via description) | batch_69f5fe58c4908190bb3a3b4fcfacba93 |
completed | May 2, 2026, 1:38 p.m. |
Created at: April 8, 2026, 9:48 p.m.