Triple
T11365352
| Position | Surface form | Disambiguated ID | Type / Status |
|---|---|---|---|
| Subject | Deligne–Lusztig theory |
E269188
|
entity |
| Predicate | studies |
P1945
|
FINISHED |
| Object | Hecke algebras |
E911207
|
NE FINISHED |
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: Hecke algebras | Statement: [Deligne–Lusztig theory, studies, Hecke algebras]
NED1
Entity disambiguation (via context triple)
gpt-5-mini-2025-08-07
Target entity: Hecke algebras Context triple: [Deligne–Lusztig theory, studies, Hecke algebras]
-
A.
Hecke algebra
chosen
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.
-
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.
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.
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.
-
E.
Temperley–Lieb algebra
The Temperley–Lieb algebra is a diagrammatic algebra arising in statistical mechanics and knot theory, central to the study of exactly solvable models and link invariants.
- F. None of above.
- G. Unsure - the case is ambiguous/there is not enough information to decide.
Provenance (3 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_69d6aacca1048190b39dbbc2174616fa |
completed | April 8, 2026, 7:21 p.m. |
| NER | Named-entity recognition | batch_69d7ea4589908190948a8225768e1eec |
completed | April 9, 2026, 6:04 p.m. |
| NED1 | Entity disambiguation (via context triple) | batch_69e55667d4908190b6290135eba41e54 |
completed | April 19, 2026, 10:25 p.m. |
Created at: April 8, 2026, 9:33 p.m.