Triple

T20509329
Position Surface form Disambiguated ID Type / Status
Subject Weyl denominator E503517 entity
Predicate relatedTo P37 FINISHED
Object Weyl integration formula
The Weyl integration formula is a fundamental result in representation theory and Lie group theory that expresses integration of class functions over a compact Lie group in terms of integration over a maximal torus with a specific Jacobian factor.
E1435395 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 integration formula | Statement: [Weyl denominator, relatedTo, Weyl integration formula]
NED1 Entity disambiguation (via context triple) gpt-5-mini-2025-08-07
Target entity: Weyl integration formula
Context triple: [Weyl denominator, relatedTo, Weyl integration formula]
  • A. 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.
  • B. 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.
  • C. 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.
  • D. Harish-Chandra character formula
    The Harish-Chandra character formula is a fundamental result in representation theory that gives an explicit expression for the characters of irreducible admissible representations of real reductive Lie groups.
  • E. Weyl group
    A Weyl group is a finite reflection group associated with a root system that encodes the symmetries of Lie algebras and Lie groups in representation theory and geometry.
  • 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 integration formula
Triple: [Weyl denominator, relatedTo, Weyl integration formula]
Generated description
The Weyl integration formula is a fundamental result in representation theory and Lie group theory that expresses integration of class functions over a compact Lie group in terms of integration over a maximal torus with a specific Jacobian factor.
NED2 Entity disambiguation (via description) gpt-5-mini-2025-08-07
Target entity: Weyl integration formula
Target entity description: The Weyl integration formula is a fundamental result in representation theory and Lie group theory that expresses integration of class functions over a compact Lie group in terms of integration over a maximal torus with a specific Jacobian factor.
  • A. 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.
  • B. 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.
  • C. 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.
  • D. Harish-Chandra character formula
    The Harish-Chandra character formula is a fundamental result in representation theory that gives an explicit expression for the characters of irreducible admissible representations of real reductive Lie groups.
  • E. Weyl group
    A Weyl group is a finite reflection group associated with a root system that encodes the symmetries of Lie algebras and Lie groups in representation theory and geometry.
  • 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_6a089d36f4688190a084267f85744cc0 completed May 16, 2026, 4:37 p.m.
NEDg Description generation batch_6a089de26d548190882d6685aaa7f5fa completed May 16, 2026, 4:40 p.m.
NED2 Entity disambiguation (via description) batch_6a089e5c696881909d1d793b884464a1 completed May 16, 2026, 4:42 p.m.
Created at: April 16, 2026, 11:36 a.m.