scholarly journals $D$-modules and representation theory of Lie groups

1993 ◽  
Vol 43 (5) ◽  
pp. 1597-1618 ◽  
Author(s):  
Masaki Kashiwara
Keyword(s):  
Representation Theory ◽  
Lie Groups ◽  
D Modules

scholarly journals Corrigendum: Analytic representation theory of Lie groups: general theory and analytic globalizations of Harish-Chandra modules

2017 ◽  
Vol 153 (1) ◽  
pp. 214-217
Author(s):  
Heiko Gimperlein ◽  
Bernhard Krötz ◽  
Henrik Schlichtkrull
Keyword(s):  
General Theory ◽  
Representation Theory ◽  
Lie Groups ◽  
Analytic Representation ◽  
Corrected Proof ◽  
Intermediate Results

We correct the proof of the main result of the paper, Theorem 5.7. Our corrected proof relies on weaker versions of a number of intermediate results from the paper. The original, more general, versions of these statements are not known to be true.

scholarly journals Studying in Lee groups and most important examples of it (Heisenberg group): دراسة في زمر لي وأهم الأمثلة عنها (زمرة هايزنبرغ)

2020 ◽  
Vol 4 (1) ◽  
Author(s):  
Soha Ali Salamah
Keyword(s):  
Number Theory ◽  
Partial Differential Equations ◽  
Differential Equations ◽  
Representation Theory ◽  
Heisenberg Group ◽  
Harmonic Analysis ◽  
Lie Groups ◽  
General Definition ◽  
Nilpotent Lie Groups ◽  
Basic Facts

In this research, we present some basic facts about Lie algebra and Lie groups. We shall require only elementary facts about the general definition and knowledge of a few of the more basic groups, such as Euclidean groups. Then we introduce the Heisenberg group which is the most well-known example from the realm of nilpotent Lie groups and plays an important role in several branches of mathematics, such as representation theory, partial differential equations and number theory... It also offers the greatest opportunity for generalizing the remarkable results of Euclidean harmonic analysis.

Heisenberg–Pauli–Weyl inequality for connected nilpotent Lie groups

2018 ◽  
Vol 29 (12) ◽  
pp. 1850086 ◽  
Author(s):  
Kais Smaoui
Keyword(s):  
Representation Theory ◽  
Lie Groups ◽  
Plancherel Formula ◽  
Nilpotent Lie Groups ◽  
Weyl Inequality ◽  
Uncertainty Inequality

The purpose of this paper is to formulate and prove an analogue of the classical Heisenberg–Pauli–Weyl uncertainty inequality for connected nilpotent Lie groups with noncompact center. Representation theory and a localized Plancherel formula play an important role in the proof.

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