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

2011 ◽  
Vol 147 (5) ◽  
pp. 1581-1607 ◽  
Author(s):  
Heiko Gimperlein ◽  
Bernhard Krötz ◽  
Henrik Schlichtkrull
Keyword(s):  
General Theory ◽  
Representation Theory ◽  
Lie Groups ◽  
Lie Group ◽  
Analytic Functions ◽  
General Framework ◽  
Analytic Representation ◽  
Reductive Groups ◽  
Topological Properties ◽  
Rapid Decay

AbstractIn this article a general framework for studying analytic representations of a real Lie group G is introduced. Fundamental topological properties of the representations are analyzed. A notion of temperedness for analytic representations is introduced, which indicates the existence of an action of a certain natural algebra 𝒜(G) of analytic functions of rapid decay. For reductive groups every Harish-Chandra module V is shown to admit a unique tempered analytic globalization, which is generated by V and 𝒜(G) and which embeds as the space of analytic vectors in all Banach globalizations of V.

UNIVERSAL CENTRAL EXTENSIONS

1994 ◽  
Vol 06 (02) ◽  
pp. 207-225 ◽  
Author(s):  
M. S. RAGHUNATHAN
Keyword(s):  
General Theory ◽  
Lie Groups ◽  
Abelian Groups ◽  
Central Extensions ◽  
Universal Central Extensions

The following is an account, self-contained and essentially expository, of the general theory of universal central extensions of groups with applications to some important classes of groups: perfect groups, abelian groups and connected Lie groups. The notation is occasionally different from that in the text — this should not cause any confusion.

scholarly journals Canonical bases and higher representation theory

2014 ◽  
Vol 151 (1) ◽  
pp. 121-166 ◽  
Author(s):  
Ben Webster
Keyword(s):  
General Theory ◽  
Representation Theory ◽  
Finite Type ◽  
Canonical Basis ◽  
Canonical Bases ◽  
Enveloping Algebra ◽  
Highest Weight ◽  
Natural Categories ◽  
Grothendieck Groups ◽  
Quantized Universal Enveloping Algebra

AbstractThis paper develops a general theory of canonical bases and how they arise naturally in the context of categorification. As an application, we show that Lusztig’s canonical basis in the whole quantized universal enveloping algebra is given by the classes of the indecomposable 1-morphisms in a categorification when the associated Lie algebra is of finite type and simply laced. We also introduce natural categories whose Grothendieck groups correspond to the tensor products of lowest- and highest-weight integrable representations. This generalizes past work of the author’s in the highest-weight case.

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.

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