Triple

T11365347
Position Surface form Disambiguated ID Type / Status
Subject Deligne–Lusztig theory E269188 entity
Predicate basedOn P98 FINISHED
Object Deligne–Lusztig varieties
Deligne–Lusztig varieties are certain algebraic varieties associated with finite groups of Lie type that play a central role in constructing and understanding their complex representations.
E269188 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: Deligne–Lusztig varieties | Statement: [Deligne–Lusztig theory, basedOn, Deligne–Lusztig varieties]
NED1 Entity disambiguation (via context triple) gpt-5-mini-2025-08-07
Target entity: Deligne–Lusztig varieties
Context triple: [Deligne–Lusztig theory, basedOn, Deligne–Lusztig varieties]
  • A. 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.
  • B. Shimura varieties
    Shimura varieties are higher-dimensional algebraic varieties that generalize modular curves and play a central role in the Langlands program by connecting number theory, automorphic forms, and arithmetic geometry.
  • C. Real Reductive Groups II
    Real Reductive Groups II is a graduate-level mathematics monograph by Nolan Wallach that develops the representation theory and harmonic analysis of real reductive Lie groups in depth.
  • D. 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.
  • E. Real Reductive Groups I
    Real Reductive Groups I is a foundational mathematical monograph by Nolan Wallach that develops the representation theory and harmonic analysis 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: Deligne–Lusztig varieties
Triple: [Deligne–Lusztig theory, basedOn, Deligne–Lusztig varieties]
Generated description
Deligne–Lusztig varieties are certain algebraic varieties associated with finite groups of Lie type that play a central role in constructing and understanding their complex representations.
NED2 Entity disambiguation (via description) gpt-5-mini-2025-08-07
Target entity: Deligne–Lusztig varieties
Target entity description: Deligne–Lusztig varieties are certain algebraic varieties associated with finite groups of Lie type that play a central role in constructing and understanding their complex representations.
  • A. Deligne–Lusztig theory chosen
    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.
  • B. Shimura varieties
    Shimura varieties are higher-dimensional algebraic varieties that generalize modular curves and play a central role in the Langlands program by connecting number theory, automorphic forms, and arithmetic geometry.
  • C. Real Reductive Groups II
    Real Reductive Groups II is a graduate-level mathematics monograph by Nolan Wallach that develops the representation theory and harmonic analysis of real reductive Lie groups in depth.
  • D. 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.
  • E. Real Reductive Groups I
    Real Reductive Groups I is a foundational mathematical monograph by Nolan Wallach that develops the representation theory and harmonic analysis of real reductive Lie groups.
  • F. None of above.

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_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.
NEDg Description generation batch_69e562c6e7c8819098d22a6e0daa4a51 completed April 19, 2026, 11:18 p.m.
NED2 Entity disambiguation (via description) batch_69e56a472f0c819086c1cccaa5ca0ae7 completed April 19, 2026, 11:50 p.m.
Created at: April 8, 2026, 9:33 p.m.