Triple

T23235057
Position Surface form Disambiguated ID Type / Status
Subject Verma module E581261 entity
Predicate relatedConcept P37 FINISHED
Object Weyl module
A Weyl module is a finite-dimensional highest-weight representation of a semisimple Lie algebra (or algebraic group) that plays a central role in the classification and study of their representations.
E1576273 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: Weyl module | Statement: [Verma module, relatedConcept, Weyl module]
NED1 Entity disambiguation (via context triple) gpt-5-mini-2025-08-07
Target entity: Weyl module
Context triple: [Verma module, relatedConcept, Weyl module]
  • A. Verma module
    A Verma module is a type of highest-weight module over a Lie algebra that is freely generated from a highest-weight vector and plays a central role in the classification of representations of semisimple Lie algebras.
  • B. Weyl character formula
    The Weyl character formula is a fundamental result in representation theory that gives an explicit expression for the characters of irreducible finite-dimensional representations of semisimple Lie algebras and Lie groups.
  • C. Weyl dimension formula
    The Weyl dimension formula is a fundamental result in representation theory that gives an explicit product expression for the dimension of each finite-dimensional irreducible representation of a semisimple Lie algebra or compact Lie group in terms of its highest weight and the root system.
  • D. Weyl vector
    The Weyl vector is a distinguished element in the weight space of a semisimple Lie algebra, defined as half the sum of all positive roots and playing a central role in representation theory and the Weyl character formula.
  • E. Weyl denominator
    The Weyl denominator is a key product expression in Lie theory that appears in the Weyl character formula, encoding the alternating sum over the Weyl group and playing a central role in describing characters of irreducible representations of semisimple Lie algebras.
  • 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: Weyl module
Triple: [Verma module, relatedConcept, Weyl module]
Generated description
A Weyl module is a finite-dimensional highest-weight representation of a semisimple Lie algebra (or algebraic group) that plays a central role in the classification and study of their representations.
NED2 Entity disambiguation (via description) gpt-5-mini-2025-08-07
Target entity: Weyl module
Target entity description: A Weyl module is a finite-dimensional highest-weight representation of a semisimple Lie algebra (or algebraic group) that plays a central role in the classification and study of their representations.
  • A. Verma module
    A Verma module is a type of highest-weight module over a Lie algebra that is freely generated from a highest-weight vector and plays a central role in the classification of representations of semisimple Lie algebras.
  • B. Weyl character formula
    The Weyl character formula is a fundamental result in representation theory that gives an explicit expression for the characters of irreducible finite-dimensional representations of semisimple Lie algebras and Lie groups.
  • C. Weyl dimension formula
    The Weyl dimension formula is a fundamental result in representation theory that gives an explicit product expression for the dimension of each finite-dimensional irreducible representation of a semisimple Lie algebra or compact Lie group in terms of its highest weight and the root system.
  • D. Weyl vector
    The Weyl vector is a distinguished element in the weight space of a semisimple Lie algebra, defined as half the sum of all positive roots and playing a central role in representation theory and the Weyl character formula.
  • E. Weyl denominator
    The Weyl denominator is a key product expression in Lie theory that appears in the Weyl character formula, encoding the alternating sum over the Weyl group and playing a central role in describing characters of irreducible representations of semisimple Lie algebras.
  • 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_69e2460556f88190be1744a84a84173f completed April 17, 2026, 2:39 p.m.
NER Named-entity recognition batch_69f192e8c7548190b53434eeb2620a6e completed April 29, 2026, 5:11 a.m.
NED1 Entity disambiguation (via context triple) batch_6a0c3f59de808190afb414450ac32d0d completed May 19, 2026, 10:45 a.m.
NEDg Description generation batch_6a0c4008c4a881908ad49e733b549036 completed May 19, 2026, 10:48 a.m.
NED2 Entity disambiguation (via description) batch_6a0c40bece448190bb9fd1a3058a1f06 completed May 19, 2026, 10:51 a.m.
Created at: April 17, 2026, 4:09 p.m.