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.