The length spectrum and representation theory on two- and three-step nilpotent Lie groups

1994 ◽  
pp. 133-155 ◽  
Author(s):  
Ruth Gornet
Keyword(s):  
Representation Theory ◽  
Lie Groups ◽  
Length Spectrum ◽  
Nilpotent Lie Groups

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.

scholarly journals An invariant for unitary representations of nilpotent Lie groups.

1987 ◽  
Vol 34 (1) ◽  
pp. 23-30 ◽  
Author(s):  
C. Benson ◽  
G. Ratcliff
Keyword(s):  
Lie Groups ◽  
Unitary Representations ◽  
Nilpotent Lie Groups
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