Theory of Lie groups

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The theorem of Iwasawa. Finitely presented Lie algebras. Free Lie algebras.

Contructing a basis of a finitely presented Lie algebra. Hall sets. Standard sequences. A Hall set provides a basis. Two examples of Hall orders. Reduction in L X. Presentations of the simple Lie algebras of characteristic zero. Representations of semisimple Lie algebras. The weights of a representation. Verma modules. Integral functions and the Weyl group. Finite dimensionality.

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On representing the weights. Computing orbits of the Weyl group. Calculating the weights. The multiplicity formula of Freudenthal. Modifying Freudenthal's formula.

Representation Theory of Lie Groups and Lie Algebras

Weyl's formulas. The formulas of Kostant and Racah. Decomposing a tensor product. Branching rules. On associative algebras. Radical and semisimplicity. Algebras generated by a single element. Central idempotents. Index of Symbols.

Integrable random systems, representation theory and geometry of Lie groups

Index of Terminology. Index of Algorithms. The aim of the present work is two-fold. Firstly it aims at a giving an account of many existing algorithms for calculating with finite-dimensional Lie algebras. Secondly, the book provides an introduction into the theory of finite-dimensional Lie algebras. These two subject areas are intimately related. First of all, the algorithmic perspective often invites a different approach to the theoretical material than the one taken in various other monographs e.

Also proofs that contain algorithmic constructions are explicitly formulated as algorithms an example is the isomorphism theorem for semisimple Lie algebras that constructs an isomorphism in case it exists. Secondly, the algorithms can be used to arrive at a better understanding of the theory. Performing the algorithms in concrete examples, calculating with the concepts involved, really brings the theory of life.

It is one of the first books which combines both these aspects in one volume. The book is well written and the material is clearly presented. We are always looking for ways to improve customer experience on Elsevier. We would like to ask you for a moment of your time to fill in a short questionnaire, at the end of your visit.

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Authors: W. Hardcover ISBN: Imprint: North Holland. Published Date: 4th February Page Count: View all volumes in this series: North-Holland Mathematical Library.

Lie groups and Lie algebras

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What is a Lie group?

Your review was sent successfully and is now waiting for our team to publish it. Reviews 0. Updating Results. Representation of p-adic Groups - The most exciting recent progresses are the proof of the Local Langlands Conjecture and the new constructions of discrete series representations. The latter topic can be traced to the fundamental work of Roger Howe. For the Local Langlands Conjecture, the current proof involves tools from number theory and algebraic geometry and represent a new set of promising ideas that may continue to bear fruits in the near future.

Unitary Representation of Real Reductive Groups - One of the most fundamental problems in representation theory is to understand the unitary dual of a real reductive group. While there were remarkable progresses in the last few decades such as Harish-Chandra's work on discrete series, the mystery of the unitary dual very much remains.

Topics covered in this sub theme will include the orbit method and its ramifications, for instance, understanding the unitary dual through wavefront sets and other related invariants. As much of the mystery involves singular unitary representations, the subject will also be featured prominently.

Multiplicity-Free Actions and Representations - Multiplicity -free actions are those group actions, which have simple spectrum. On the one hand, they are special enough to allow a deeper understanding, even permitting classifications in certain contexts.

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On the other hand, many interesting representations of Lie groups are often multiplicity-free as representations of other groups such as the maximal compact subgroups. In this sub theme, we will explore the intimate link between the theory of multiplicity-free actions, invariant theory and representation theory.