Triple

T20508997
Position Surface form Disambiguated ID Type / Status
Subject Schur–Weyl duality E503508 entity
Predicate uses P98 FINISHED
Object Schur functors
Schur functors are algebraic constructions that associate to each partition a functor from vector spaces to representations, encoding polynomial representations of general linear groups and symmetric group actions.
E1436426 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: Schur functors | Statement: [Schur–Weyl duality, uses, Schur functors]
NED1 Entity disambiguation (via context triple) gpt-5-mini-2025-08-07
Target entity: Schur functors
Context triple: [Schur–Weyl duality, uses, Schur functors]
  • A. 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.
  • B. Gelfand–Tsetlin algebra
    The Gelfand–Tsetlin algebra is a commutative subalgebra of the universal enveloping algebra of a Lie algebra that acts diagonally in the Gelfand–Tsetlin basis and plays a central role in the explicit description of representations.
  • C. 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.
  • D. Macdonald polynomials
    Macdonald polynomials are a family of orthogonal symmetric functions depending on two parameters that generalize several classical symmetric polynomials, such as Schur and Jack polynomials, and play a central role in algebraic combinatorics and representation theory.
  • E. Gelfand–Tsetlin basis
    The Gelfand–Tsetlin basis is a canonical, combinatorially defined basis for representations of certain Lie algebras and groups, particularly used in the representation theory of GL(n) and related structures.
  • 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: Schur functors
Triple: [Schur–Weyl duality, uses, Schur functors]
Generated description
Schur functors are algebraic constructions that associate to each partition a functor from vector spaces to representations, encoding polynomial representations of general linear groups and symmetric group actions.
NED2 Entity disambiguation (via description) gpt-5-mini-2025-08-07
Target entity: Schur functors
Target entity description: Schur functors are algebraic constructions that associate to each partition a functor from vector spaces to representations, encoding polynomial representations of general linear groups and symmetric group actions.
  • A. 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.
  • B. Gelfand–Tsetlin algebra
    The Gelfand–Tsetlin algebra is a commutative subalgebra of the universal enveloping algebra of a Lie algebra that acts diagonally in the Gelfand–Tsetlin basis and plays a central role in the explicit description of representations.
  • C. 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.
  • D. Macdonald polynomials
    Macdonald polynomials are a family of orthogonal symmetric functions depending on two parameters that generalize several classical symmetric polynomials, such as Schur and Jack polynomials, and play a central role in algebraic combinatorics and representation theory.
  • E. Gelfand–Tsetlin basis
    The Gelfand–Tsetlin basis is a canonical, combinatorially defined basis for representations of certain Lie algebras and groups, particularly used in the representation theory of GL(n) and related structures.
  • 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_69e0b4b1e52c8190894281cf7e3283ab completed April 16, 2026, 10:06 a.m.
NER Named-entity recognition batch_69e69dc9de788190882ce471966ef2b4 completed April 20, 2026, 9:42 p.m.
NED1 Entity disambiguation (via context triple) batch_6a089d34c4ac8190a4ff8d8442dac927 completed May 16, 2026, 4:37 p.m.
NEDg Description generation batch_6a089dc1a5688190ba700d78fb1b1940 completed May 16, 2026, 4:39 p.m.
NED2 Entity disambiguation (via description) batch_6a08a16aa21c8190aa7d79578aca0698 completed May 16, 2026, 4:55 p.m.
Created at: April 16, 2026, 11:36 a.m.