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 (1)
| Label | Occurrences |
|---|---|
| Real Reductive Groups II canonical | 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]
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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.
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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
NERFINISHED
ⓘ
Nolan Wallach NERFINISHED ⓘ |
| emphasis |
classification of irreducible representations
ⓘ
detailed proofs ⓘ structural theory of real reductive groups ⓘ |
| field |
Lie theory
ⓘ
harmonic analysis ⓘ real reductive Lie groups NERFINISHED ⓘ representation theory ⓘ |
| language | English ⓘ |
| level | advanced graduate ⓘ |
| partOf | Real Reductive Groups NERFINISHED ⓘ |
| prequel | Real Reductive Groups I NERFINISHED ⓘ |
| 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 NERFINISHED ⓘ Harish-Chandra modules NERFINISHED ⓘ Langlands classification NERFINISHED ⓘ 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
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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 (1)
Full triples — surface form annotated when it differs from this entity's canonical label.