Triple

T20509239
Position Surface form Disambiguated ID Type / Status
Subject Kazhdan–Lusztig theory E503515 entity
Predicate relatedTo P37 FINISHED
Object Soergel bimodules
Soergel bimodules are certain graded bimodules over polynomial rings that categorify Hecke algebras and provide a powerful geometric and algebraic framework for understanding Kazhdan–Lusztig theory and representation theory of Coxeter groups.
E1436432 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: Soergel bimodules | Statement: [Kazhdan–Lusztig theory, relatedTo, Soergel bimodules]
NED1 Entity disambiguation (via context triple) gpt-5-mini-2025-08-07
Target entity: Soergel bimodules
Context triple: [Kazhdan–Lusztig theory, relatedTo, Soergel bimodules]
  • A. 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.
  • B. 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.
  • C. Beilinson–Bernstein localization theorem
    The Beilinson–Bernstein localization theorem is a fundamental result in geometric representation theory that realizes representations of semisimple Lie algebras as sheaves of differential operators on flag varieties, establishing an equivalence between algebraic and geometric categories.
  • 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. Bernstein center in representation theory
    The Bernstein center in representation theory is a commutative algebra that acts as the center of the category of smooth representations of a p-adic reductive group, playing a key role in decomposing and classifying these representations.
  • 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: Soergel bimodules
Triple: [Kazhdan–Lusztig theory, relatedTo, Soergel bimodules]
Generated description
Soergel bimodules are certain graded bimodules over polynomial rings that categorify Hecke algebras and provide a powerful geometric and algebraic framework for understanding Kazhdan–Lusztig theory and representation theory of Coxeter groups.
NED2 Entity disambiguation (via description) gpt-5-mini-2025-08-07
Target entity: Soergel bimodules
Target entity description: Soergel bimodules are certain graded bimodules over polynomial rings that categorify Hecke algebras and provide a powerful geometric and algebraic framework for understanding Kazhdan–Lusztig theory and representation theory of Coxeter groups.
  • A. 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.
  • B. 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.
  • C. Beilinson–Bernstein localization theorem
    The Beilinson–Bernstein localization theorem is a fundamental result in geometric representation theory that realizes representations of semisimple Lie algebras as sheaves of differential operators on flag varieties, establishing an equivalence between algebraic and geometric categories.
  • 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. Bernstein center in representation theory
    The Bernstein center in representation theory is a commutative algebra that acts as the center of the category of smooth representations of a p-adic reductive group, playing a key role in decomposing and classifying these representations.
  • 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.