Real Reductive Groups I
E893437
Real Reductive Groups I is a foundational mathematical monograph by Nolan Wallach that develops the representation theory and harmonic analysis of real reductive Lie groups.
All labels observed (2)
| Label | Occurrences |
|---|---|
| Real Reductive Groups I canonical | 2 |
| Real Reductive Groups | 1 |
How this entity was disambiguated
This entity first appeared as the object of triple T10931402 — 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: Real Reductive Groups I Context triple: [Nolan Wallach, hasWrittenWork, Real Reductive Groups I]
-
A.
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.
-
B.
The Classical Groups: Their Invariants and Representations
The Classical Groups: Their Invariants and Representations is a foundational mathematical monograph by Hermann Weyl that systematically develops the theory of classical Lie groups, their invariants, and their representation theory.
-
C.
Algebraic Groups and Class Fields
"Algebraic Groups and Class Fields" is a influential mathematical monograph that develops the deep connections between algebraic group theory and class field theory within number theory and arithmetic geometry.
-
D.
Adeles and Algebraic Groups
"Adeles and Algebraic Groups" is a foundational mathematical work by André Weil that develops the theory of adeles and its deep connections with algebraic groups and number theory.
-
E.
Paley–Wiener theorem for real reductive groups
The Paley–Wiener theorem for real reductive groups is a fundamental result in harmonic analysis that characterizes the image of compactly supported smooth functions under the group Fourier transform in terms of holomorphic functions with specific growth and support conditions.
- 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: Real Reductive Groups I Target entity description: Real Reductive Groups I is a foundational mathematical monograph by Nolan Wallach that develops the representation theory and harmonic analysis of real reductive Lie groups.
-
A.
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.
-
B.
The Classical Groups: Their Invariants and Representations
The Classical Groups: Their Invariants and Representations is a foundational mathematical monograph by Hermann Weyl that systematically develops the theory of classical Lie groups, their invariants, and their representation theory.
-
C.
Algebraic Groups and Class Fields
"Algebraic Groups and Class Fields" is a influential mathematical monograph that develops the deep connections between algebraic group theory and class field theory within number theory and arithmetic geometry.
-
D.
Adeles and Algebraic Groups
"Adeles and Algebraic Groups" is a foundational mathematical work by André Weil that develops the theory of adeles and its deep connections with algebraic groups and number theory.
-
E.
Paley–Wiener theorem for real reductive groups
The Paley–Wiener theorem for real reductive groups is a fundamental result in harmonic analysis that characterizes the image of compactly supported smooth functions under the group Fourier transform in terms of holomorphic functions with specific growth and support conditions.
- F. None of above. chosen
Statements (34)
| Predicate | Object |
|---|---|
| instanceOf |
book
ⓘ
mathematical monograph ⓘ nonfiction work ⓘ |
| audience |
graduate students in mathematics
ⓘ
research mathematicians ⓘ |
| author |
Nolan R. Wallach
ⓘ
linked to:
Nolan Wallach
Nolan Wallach ⓘ |
| field |
Lie theory
ⓘ
harmonic analysis ⓘ representation theory ⓘ |
| focus |
foundations of harmonic analysis on real reductive Lie groups
ⓘ
foundations of representation theory of real reductive Lie groups ⓘ |
| genre | research monograph ⓘ |
| hasPart | Real Reductive Groups II ⓘ |
| influenced |
harmonic analysis on semisimple Lie groups
ⓘ
modern representation theory of real Lie groups ⓘ |
| isPartOf |
Real Reductive Groups
ⓘ
linked to:
Real Reductive Groups I
|
| language | English ⓘ |
| subject |
(g,K)-modules
ⓘ
Cartan decomposition ⓘ Harish-Chandra modules ⓘ Iwasawa decomposition ⓘ Plancherel formula ⓘ globalizations of Harish-Chandra modules ⓘ harmonic analysis on real reductive groups ⓘ invariant differential operators ⓘ parabolic induction ⓘ principal series representations ⓘ real reductive Lie groups ⓘ spherical functions ⓘ structure theory of real reductive Lie groups ⓘ tempered representations ⓘ unitary representations ⓘ |
| volumeNumber | 1 ⓘ |
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: Real Reductive Groups I Description of subject: Real Reductive Groups I is a foundational mathematical monograph by Nolan Wallach that develops the representation theory and harmonic analysis of real reductive Lie groups.
Referenced by (3)
Full triples — surface form annotated when it differs from this entity's canonical label.
linked to: Real Reductive Groups I