Triple

T11576264
Position Surface form Disambiguated ID Type / Status
Subject Joseph Bernstein E274511 entity
Predicate notableWork P4 FINISHED
Object 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.
E934437 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: Bernstein center in representation theory | Statement: [Joseph Bernstein, notableWork, Bernstein center in representation theory]
NED1 Entity disambiguation (via context triple) gpt-5-mini-2025-08-07
Target entity: Bernstein center in representation theory
Context triple: [Joseph Bernstein, notableWork, Bernstein center 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. Kazhdan–Lusztig theory
    Kazhdan–Lusztig theory is a framework in representation theory and algebraic geometry that studies Hecke algebras and their bases via Kazhdan–Lusztig polynomials, with deep connections to the representation theory of Lie algebras and geometry of Schubert varieties.
  • C. Representations of groups
    Representations of groups is a branch of mathematics that studies how abstract groups can act as linear transformations on vector spaces, typically via homomorphisms into groups of matrices.
  • 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. 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.
  • 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: Bernstein center in representation theory
Triple: [Joseph Bernstein, notableWork, Bernstein center in representation theory]
Generated description
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.
NED2 Entity disambiguation (via description) gpt-5-mini-2025-08-07
Target entity: Bernstein center in representation theory
Target entity description: 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.
  • 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. Kazhdan–Lusztig theory
    Kazhdan–Lusztig theory is a framework in representation theory and algebraic geometry that studies Hecke algebras and their bases via Kazhdan–Lusztig polynomials, with deep connections to the representation theory of Lie algebras and geometry of Schubert varieties.
  • C. Representations of groups
    Representations of groups is a branch of mathematics that studies how abstract groups can act as linear transformations on vector spaces, typically via homomorphisms into groups of matrices.
  • 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. 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.
  • 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_69d6aae5ac3c81908d2b0a3a665665b2 completed April 8, 2026, 7:22 p.m.
NER Named-entity recognition batch_69d89049721081909278adfada668ef9 completed April 10, 2026, 5:53 a.m.
NED1 Entity disambiguation (via context triple) batch_69e713f7ca4c81908f29143df420fd71 completed April 21, 2026, 6:06 a.m.
NEDg Description generation batch_69e720f9a8588190aa766d2e1628207a completed April 21, 2026, 7:02 a.m.
NED2 Entity disambiguation (via description) batch_69e72315dda08190996aa84587c5fc80 completed April 21, 2026, 7:11 a.m.
Created at: April 8, 2026, 9:38 p.m.