Triple
T20509002
| Position | Surface form | Disambiguated ID | Type / Status |
|---|---|---|---|
| Subject | Schur–Weyl duality |
E503508
|
entity |
| Predicate | hasVariant |
P455
|
FINISHED |
| Object | Schur–Weyl duality for Hecke algebras |
—
|
NE NERFINISHED |
How this triple was built (2 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–Weyl duality for Hecke algebras | Statement: [Schur–Weyl duality, hasVariant, Schur–Weyl duality for Hecke algebras]
NED1
Entity disambiguation (via context triple)
gpt-5-mini-2025-08-07
Target entity: Schur–Weyl duality for Hecke algebras Context triple: [Schur–Weyl duality, hasVariant, Schur–Weyl duality for Hecke algebras]
-
A.
Schur–Weyl duality
chosen
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.
Hecke algebra
A Hecke algebra is a deformation of a group algebra (often of a Coxeter or Weyl group) that plays a central role in representation theory, algebraic combinatorics, and the study of quantum groups and integrable systems.
-
C.
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.
-
D.
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.
-
E.
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.
- F. None of above.
- G. Unsure - the case is ambiguous/there is not enough information to decide.
Provenance (2 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. |
Created at: April 16, 2026, 11:36 a.m.