Triple
T11365356
| Position | Surface form | Disambiguated ID | Type / Status |
|---|---|---|---|
| Subject | Deligne–Lusztig theory |
E269188
|
entity |
| Predicate | relatesTo |
P37
|
FINISHED |
| Object |
Springer correspondence
The Springer correspondence is a fundamental result in geometric representation theory that links representations of Weyl groups to the geometry of nilpotent orbits in Lie algebras via the cohomology of Springer fibers.
|
E921612
|
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: Springer correspondence | Statement: [Deligne–Lusztig theory, relatesTo, Springer correspondence]
NED1
Entity disambiguation (via context triple)
gpt-5-mini-2025-08-07
Target entity: Springer correspondence Context triple: [Deligne–Lusztig theory, relatesTo, Springer correspondence]
-
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.
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.
-
C.
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.
-
D.
Deligne–Lusztig theory
Deligne–Lusztig theory is a framework in algebraic geometry and representation theory that constructs and studies representations of finite groups of Lie type using varieties defined over finite fields.
-
E.
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.
- 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: Springer correspondence Triple: [Deligne–Lusztig theory, relatesTo, Springer correspondence]
Generated description
The Springer correspondence is a fundamental result in geometric representation theory that links representations of Weyl groups to the geometry of nilpotent orbits in Lie algebras via the cohomology of Springer fibers.
NED2
Entity disambiguation (via description)
gpt-5-mini-2025-08-07
Target entity: Springer correspondence Target entity description: The Springer correspondence is a fundamental result in geometric representation theory that links representations of Weyl groups to the geometry of nilpotent orbits in Lie algebras via the cohomology of Springer fibers.
-
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.
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.
-
C.
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.
-
D.
Deligne–Lusztig theory
Deligne–Lusztig theory is a framework in algebraic geometry and representation theory that constructs and studies representations of finite groups of Lie type using varieties defined over finite fields.
-
E.
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.
- 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_69d6aacca1048190b39dbbc2174616fa |
completed | April 8, 2026, 7:21 p.m. |
| NER | Named-entity recognition | batch_69d7ea4589908190948a8225768e1eec |
completed | April 9, 2026, 6:04 p.m. |
| NED1 | Entity disambiguation (via context triple) | batch_69e55667d4908190b6290135eba41e54 |
completed | April 19, 2026, 10:25 p.m. |
| NEDg | Description generation | batch_69e562c6e7c8819098d22a6e0daa4a51 |
completed | April 19, 2026, 11:18 p.m. |
| NED2 | Entity disambiguation (via description) | batch_69e56a472f0c819086c1cccaa5ca0ae7 |
completed | April 19, 2026, 11:50 p.m. |
Created at: April 8, 2026, 9:33 p.m.