Bernstein center
E934441
The Bernstein center is a fundamental object in the representation theory of p-adic groups that parametrizes and controls the decomposition of smooth representations into blocks.
All labels observed (1)
| Label | Occurrences |
|---|---|
| Bernstein center canonical | 2 |
How this entity was disambiguated
This entity first appeared as the object of triple T11576293 — resolving that mention is where its identity was fixed. The disambiguator weighed these candidate entities and picked the highlighted one (or “None”, minting a new entity). This is how homonymy is resolved: the same surface form can point to different entities.
NED1
Entity disambiguation (via context triple)
gpt-5-mini-2025-08-07
Target entity: Bernstein center Context triple: [Joseph Bernstein, notableConcept, Bernstein center]
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A.
Regenstrief Institute
Regenstrief Institute is a medical research organization known for its pioneering work in health informatics and the development of widely used clinical data standards.
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B.
Osnabruck Centre
Osnabruck Centre is a small rural community located within the Township of South Stormont in eastern Ontario, Canada.
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C.
Vienna Biocenter
The Vienna Biocenter is a major life sciences research and education campus in Vienna, Austria, hosting leading academic institutes and biotech companies focused on molecular biology and related fields.
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D.
University of Bonn
The University of Bonn is a major public research university in Bonn, Germany, renowned for its strong programs in the humanities and sciences and its long tradition of scholarly excellence.
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E.
Helmholtz Association
The Helmholtz Association is Germany’s largest scientific research organization, operating a network of national research centers that conduct long-term, large-scale research in areas such as energy, health, environment, and technology.
- F. None of above. chosen
- G. Unsure - the case is ambiguous/there is not enough information to decide.
NED2
Entity disambiguation (via description)
gpt-5-mini-2025-08-07
Target entity: Bernstein center Target entity description: The Bernstein center is a fundamental object in the representation theory of p-adic groups that parametrizes and controls the decomposition of smooth representations into blocks.
-
A.
Regenstrief Institute
Regenstrief Institute is a medical research organization known for its pioneering work in health informatics and the development of widely used clinical data standards.
-
B.
Osnabruck Centre
Osnabruck Centre is a small rural community located within the Township of South Stormont in eastern Ontario, Canada.
-
C.
Vienna Biocenter
The Vienna Biocenter is a major life sciences research and education campus in Vienna, Austria, hosting leading academic institutes and biotech companies focused on molecular biology and related fields.
-
D.
University of Bonn
The University of Bonn is a major public research university in Bonn, Germany, renowned for its strong programs in the humanities and sciences and its long tradition of scholarly excellence.
-
E.
Helmholtz Association
The Helmholtz Association is Germany’s largest scientific research organization, operating a network of national research centers that conduct long-term, large-scale research in areas such as energy, health, environment, and technology.
- F. None of above. chosen
Statements (31)
| Predicate | Object |
|---|---|
| instanceOf |
center of a category
ⓘ
mathematical object ⓘ |
| actsOn | category of smooth complex representations of a p-adic reductive group ⓘ |
| appearsIn |
representation theory of GL_n over a p-adic field
ⓘ
representation theory of classical p-adic groups ⓘ |
| context | smooth representations of reductive groups over non-Archimedean local fields ⓘ |
| controls | decomposition of smooth representations into blocks ⓘ |
| definedOver | complex numbers ⓘ |
| describedAs | algebra of central distributions on a p-adic group ⓘ |
| field |
p-adic groups
ⓘ
representation theory ⓘ |
| generalizationOf | center of the Hecke algebra in the Iwahori-spherical case ⓘ |
| hasComponent | primitive idempotents corresponding to inertial equivalence classes ⓘ |
| hasProperty |
functorial in the p-adic group
ⓘ
idempotents correspond to blocks ⓘ |
| introducedBy | Joseph Bernstein ⓘ |
| is |
algebra of endomorphisms of the identity functor on the category of smooth representations
ⓘ
commutative algebra ⓘ |
| namedAfter | Joseph Bernstein ⓘ |
| parametrizes |
Bernstein components
ⓘ
blocks of the category of smooth representations ⓘ |
| relatedTo |
Bernstein decomposition
ⓘ
Bernstein spectrum ⓘ Hecke algebras ⓘ
linked to:
Hecke algebra
cuspidal support ⓘ local Langlands program ⓘ
linked to:
local Langlands correspondence
parabolic induction ⓘ smooth dual of a p-adic group ⓘ |
| structure | spectrum decomposes into Bernstein components ⓘ |
| usedFor |
block decomposition of representation categories
ⓘ
classification of irreducible smooth representations of p-adic groups ⓘ |
How these facts were elicited
The pipeline generated the facts above by prompting gpt-5.1 with this entity's name + description and the instruction below.
Instruction
You are a knowledge base construction expert. Given a subject entity and a description of it, return factual statements that you know for the subject as a JSON list of dictionaries(triples), where keys must be "subject", "predicate" and "object". The number of facts may be very high, between 25 to 50 or more, for very popular subjects. For less popular subjects, the number of facts can be very low, like 5 or 10. # Requirements - If you don't know the subject at all, return an empty list. - If the subject is not a named entity, return an empty list. - Include at least one triple where predicate is "instanceOf". - Do not get too wordy. - Separate several objects into multiple triples with one object.
Input
Subject: Bernstein center Description of subject: The Bernstein center is a fundamental object in the representation theory of p-adic groups that parametrizes and controls the decomposition of smooth representations into blocks.
Referenced by (2)
Full triples — surface form annotated when it differs from this entity's canonical label.