Triple
T20509222
| Position | Surface form | Disambiguated ID | Type / Status |
|---|---|---|---|
| Subject | Kazhdan–Lusztig theory |
E503515
|
entity |
| Predicate | uses |
P98
|
FINISHED |
| Object | Verma modules |
—
|
NE NERFINISHED |
How this triple was built (2 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: Verma modules | Statement: [Kazhdan–Lusztig theory, uses, Verma modules]
NED1
Entity disambiguation (via context triple)
gpt-5-mini-2025-08-07
Target entity: Verma modules Context triple: [Kazhdan–Lusztig theory, uses, Verma modules]
-
A.
Verma module
chosen
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.
Harish-Chandra isomorphism
The Harish-Chandra isomorphism is a fundamental result in representation theory that identifies the center of the universal enveloping algebra of a semisimple Lie algebra with the algebra of Weyl group–invariant polynomials on a Cartan subalgebra.
-
C.
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.
-
D.
Bernstein–Zelevinsky classification
The Bernstein–Zelevinsky classification is a foundational framework in representation theory that systematically describes irreducible smooth representations of general linear groups over non-archimedean local fields.
-
E.
Kac–Moody algebras
Kac–Moody algebras are a broad class of (generally infinite-dimensional) Lie algebras defined by generalized Cartan matrices, encompassing finite-dimensional semisimple Lie algebras and their infinite-dimensional extensions used in representation theory and mathematical physics.
- F. None of above.
- G. Unsure - the case is ambiguous/there is not enough information to decide.
Provenance (2 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. |
Created at: April 16, 2026, 11:36 a.m.