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Representations of Weyl groups and their Hecke algebras on virtual character modules of a semisimple Lie group

open access: yesRepresentations of Weyl groups and their Hecke algebras on virtual character modules of a semisimple Lie group
openaire  

Representations of complex semisimple Lie groups and their real forms

1992
All the Lie algebras and Lie groups considered in this chapter are finite-dimensional; sometimes without mentioning this specifically we confine ourselves to a reductive Lie group, i.e., to a direct product of a simple group by a 1-dimensional center.
A. N. Leznov, M. V. Saveliev
openaire   +2 more sources

Representations of Semisimple Lie Groups and Their Matrix Elements

1992
One of fundamental results of the theory of finite dimensional representations is the following theorem (see, for example, reference [58] of the first volume).
N. Ja. Vilenkin, A. U. Klimyk
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Fock–Goncharov coordinates for semisimple Lie groups

, 2021
Fock and Goncharov introduced cluster ensembles, providing a framework for coordinates on varieties of surface representations into Lie groups, as well as a complete construction for groups of type $A_n$.
S. Gilles
semanticscholar   +1 more source

Beurling–Fourier Algebras of q-Deformations of Compact Semisimple Lie Groups and Complexification

International mathematics research notices
We study Beurling–Fourier algebras of $ q $-deformations of compact semisimple Lie groups. In particular, we show that the space of irreducible representations of the function algebras of their Drinfeld doubles is exhausted by the irreducible ...
Heon Lee, Christian Voigt
semanticscholar   +1 more source

Quantized semisimple Lie groups

Archiv der Mathematik
These notes present a quick introduction to the q-deformations of semisimple Lie groups from the point of view of unitary representation theory. In order to remain concrete, we concentrate entirely on the case of the lie algebra $\mathrm{sl}(2,\mathbb{C})
Rita Fioresi, R. Yuncken
semanticscholar   +1 more source

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