Real Reductive Groups II
E895039
Real Reductive Groups II is a graduate-level mathematics monograph by Nolan Wallach that develops the representation theory and harmonic analysis of real reductive Lie groups in depth.
All labels observed (2)
| Label | Occurrences |
|---|---|
| Real Reductive Groups II canonical | 2 |
| Real Reductive Groups | 1 |
How this entity was disambiguated
This entity first appeared as the object of triple T10931403 — 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 II Context triple: [Nolan Wallach, hasWrittenWork, Real Reductive Groups II]
-
A.
Real Reductive Groups I
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.
-
B.
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.
-
C.
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.
-
D.
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.
-
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 II Target entity description: Real Reductive Groups II is a graduate-level mathematics monograph by Nolan Wallach that develops the representation theory and harmonic analysis of real reductive Lie groups in depth.
-
A.
Real Reductive Groups I
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.
-
B.
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.
-
C.
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.
-
D.
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.
-
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 (42)
| Predicate | Object |
|---|---|
| instanceOf |
graduate-level textbook
ⓘ
mathematics monograph ⓘ research monograph ⓘ |
| audience |
graduate students in mathematics
ⓘ
researchers in harmonic analysis ⓘ researchers in representation theory ⓘ |
| author |
Nolan R. Wallach
ⓘ
linked to:
Nolan Wallach
Nolan Wallach ⓘ |
| emphasis |
classification of irreducible representations
ⓘ
detailed proofs ⓘ structural theory of real reductive groups ⓘ |
| field |
Lie theory
ⓘ
harmonic analysis ⓘ real reductive Lie groups ⓘ
linked to:
reductive Lie group
representation theory ⓘ |
| language | English ⓘ |
| level | advanced graduate ⓘ |
| partOf |
Real Reductive Groups
ⓘ
linked to:
Real Reductive Groups II
|
| prequel | Real Reductive Groups I ⓘ |
| prerequisite |
basic Lie groups and Lie algebras
ⓘ
functional analysis background ⓘ measure theory ⓘ |
| subjectArea |
abstract algebra
ⓘ
functional analysis ⓘ pure mathematics ⓘ |
| topic |
(g,K)-modules
ⓘ
Eisenstein series ⓘ Harish-Chandra modules ⓘ Langlands classification ⓘ Plancherel formula ⓘ characters of representations ⓘ discrete series representations ⓘ harmonic analysis on real reductive groups ⓘ intertwining operators ⓘ invariant differential operators ⓘ parabolic induction ⓘ spherical functions ⓘ tempered representations ⓘ unitary representations of real reductive groups ⓘ |
| usedIn |
graduate courses on representation theory of Lie groups
ⓘ
seminars on harmonic analysis on Lie groups ⓘ |
| volumeNumber | 2 ⓘ |
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 II Description of subject: Real Reductive Groups II is a graduate-level mathematics monograph by Nolan Wallach that develops the representation theory and harmonic analysis of real reductive Lie groups in depth.
Referenced by (3)
Full triples — surface form annotated when it differs from this entity's canonical label.
linked to: Real Reductive Groups II