Triple
T2475548
| Position | Surface form | Disambiguated ID | Type / Status |
|---|---|---|---|
| Subject | Israel Gelfand |
E55078
|
entity |
| Predicate | notableWork |
P4
|
FINISHED |
| Object |
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.
|
E270393
|
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: Methods of Representation Theory | Statement: [Israel Gelfand, notableWork, Methods of Representation Theory]
NED1
Entity disambiguation (via context triple)
gpt-5-mini-2025-08-07
Target entity: Methods of Representation Theory Context triple: [Israel Gelfand, notableWork, Methods of Representation Theory]
-
A.
The Classical Groups: Their Invariants and Representations
The Classical Groups: Their Invariants and Representations is a foundational mathematical monograph by Hermann Weyl that systematically develops the theory of classical Lie groups, their invariants, and their representation theory.
-
B.
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.
-
C.
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.
-
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.
Harish-Chandra character formula
The Harish-Chandra character formula is a fundamental result in representation theory that gives an explicit expression for the characters of irreducible admissible representations of real reductive Lie groups.
- 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: Methods of Representation Theory Triple: [Israel Gelfand, notableWork, Methods of Representation Theory]
Generated description
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.
NED2
Entity disambiguation (via description)
gpt-5-mini-2025-08-07
Target entity: Methods of Representation Theory Target entity description: 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.
-
A.
The Classical Groups: Their Invariants and Representations
The Classical Groups: Their Invariants and Representations is a foundational mathematical monograph by Hermann Weyl that systematically develops the theory of classical Lie groups, their invariants, and their representation theory.
-
B.
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.
-
C.
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.
-
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.
Harish-Chandra character formula
The Harish-Chandra character formula is a fundamental result in representation theory that gives an explicit expression for the characters of irreducible admissible representations of real reductive Lie groups.
- 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_69ab49e279e88190ab10d7248aea9d11 |
completed | March 6, 2026, 9:40 p.m. |
| NER | Named-entity recognition | batch_69abd14c8c388190bbdc486ffed6899e |
completed | March 7, 2026, 7:18 a.m. |
| NED1 | Entity disambiguation (via context triple) | batch_69af17ab837881909bf8704acf9598e4 |
completed | March 9, 2026, 6:55 p.m. |
| NEDg | Description generation | batch_69af1a8c7784819088be431513d60325 |
completed | March 9, 2026, 7:07 p.m. |
| NED2 | Entity disambiguation (via description) | batch_69af1b10738881909b296ecd3ff53c1b |
completed | March 9, 2026, 7:10 p.m. |
Created at: March 6, 2026, 9:45 p.m.