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.