Triple

T10773432
Position Surface form Disambiguated ID Type / Status
Subject Vladimir Drinfeld E254136 entity
Predicate knownFor P22 FINISHED
Object Drinfeld–Jimbo quantum groups
Drinfeld–Jimbo quantum groups are deformations of universal enveloping algebras of Lie algebras that provide a foundational algebraic framework for quantum integrable systems and modern representation theory.
E884937 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: Drinfeld–Jimbo quantum groups | Statement: [Vladimir Drinfeld, knownFor, Drinfeld–Jimbo quantum groups]
NED1 Entity disambiguation (via context triple) gpt-5-mini-2025-08-07
Target entity: Drinfeld–Jimbo quantum groups
Context triple: [Vladimir Drinfeld, knownFor, Drinfeld–Jimbo quantum groups]
  • A. 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.
  • B. Yang–Baxter equation
    The Yang–Baxter equation is a fundamental consistency condition in mathematical physics and integrable systems that underlies exactly solvable models, quantum groups, and braid group representations.
  • C. affine Lie algebras
    Affine Lie algebras are infinite-dimensional extensions of finite-dimensional simple Lie algebras that play a central role in representation theory, conformal field theory, and the study of exactly solvable models in mathematical physics.
  • D. Gelfand–Tsetlin basis
    The Gelfand–Tsetlin basis is a canonical, combinatorially defined basis for representations of certain Lie algebras and groups, particularly used in the representation theory of GL(n) and related structures.
  • 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. 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: Drinfeld–Jimbo quantum groups
Triple: [Vladimir Drinfeld, knownFor, Drinfeld–Jimbo quantum groups]
Generated description
Drinfeld–Jimbo quantum groups are deformations of universal enveloping algebras of Lie algebras that provide a foundational algebraic framework for quantum integrable systems and modern representation theory.
NED2 Entity disambiguation (via description) gpt-5-mini-2025-08-07
Target entity: Drinfeld–Jimbo quantum groups
Target entity description: Drinfeld–Jimbo quantum groups are deformations of universal enveloping algebras of Lie algebras that provide a foundational algebraic framework for quantum integrable systems and modern representation theory.
  • A. 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.
  • B. Yang–Baxter equation
    The Yang–Baxter equation is a fundamental consistency condition in mathematical physics and integrable systems that underlies exactly solvable models, quantum groups, and braid group representations.
  • C. affine Lie algebras
    Affine Lie algebras are infinite-dimensional extensions of finite-dimensional simple Lie algebras that play a central role in representation theory, conformal field theory, and the study of exactly solvable models in mathematical physics.
  • D. Gelfand–Tsetlin basis
    The Gelfand–Tsetlin basis is a canonical, combinatorially defined basis for representations of certain Lie algebras and groups, particularly used in the representation theory of GL(n) and related structures.
  • 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. 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_69d6aa5f54f4819082d0bbcb6f8797e6 completed April 8, 2026, 7:19 p.m.
NER Named-entity recognition batch_69d7329b27748190bd0e2569c7972fd1 completed April 9, 2026, 5:01 a.m.
NED1 Entity disambiguation (via context triple) batch_69de238559b48190abc759e744ab0f8e completed April 14, 2026, 11:22 a.m.
NEDg Description generation batch_69de271fb08c8190a44c547083226fd8 completed April 14, 2026, 11:38 a.m.
NED2 Entity disambiguation (via description) batch_69de2cecc24c8190a240366e0600426a completed April 14, 2026, 12:02 p.m.
Created at: April 8, 2026, 9:16 p.m.