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Lie groups

Author: Daniel Bump
Publisher: New York : Springer, [2013?] ©2013
Series: Graduate texts in mathematics, 225.
Edition/Format:   eBook : Document : English : Second editionView all editions and formats
Database:WorldCat
Summary:
"This book is intended for a one year graduate course on Lie groups and Lie algebras. The author proceeds beyond the representation theory of compact Lie groups (which is the basis of many texts) and provides a carefully chosen range of material to give the student the bigger picture. For compact Lie groups, the Peter-Weyl theorem, conjugacy of maximal tori (two proofs), Weyl character formula and more are covered.  Read more...
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Genre/Form: Electronic books
Additional Physical Format: Printed edition:
Material Type: Document, Internet resource
Document Type: Internet Resource, Computer File
All Authors / Contributors: Daniel Bump
ISBN: 9781461480242 1461480248 146148023X 9781461480235
OCLC Number: 861183180
Description: 1 online resource (xiii, 551 pages) : illustrations.
Contents: Part. I: Compact groups. Haar measure --
Schur orthogonality --
Compact operators --
The Peter-Weyl theorem --
Part. II: Lie groups fundamentals. Lie subgroups of GL (n,C) --
Vector fields --
Left-invariant vector fields --
The exponential map --
Tensors and universal properties --
The universal enveloping algebra --
Extension of scalars --
Representations of s1(2,C) --
The universal cover --
The local Frobenius theorem --
Tori --
Geodesics and maximal tori --
Topological proof of Cartan's theorem --
The Weyl integration formula --
The root system --
Examples of root systems --
Abstract Weyl groups --
The fundamental group --
Semisimple compact groups --
Highest-Weight vectors --
The Weyl character formula --
Spin --
Complexification --
Coxeter groups --
The Iwasawa decomposition --
The Bruhat decomposition --
Symmetric spaces --
Relative root systems --
Embeddings of lie groups --
Part. III: Topics. Mackey theory --
Characters of GL(n,C) --
Duality between Sk and GL(n, C) --
The Jacobi-Trudi identity --
Schur polynomials and GL(n,C) --
Schur polynomials and Sk --
Random matrix theory --
Minors of Toeplitz matrices --
Branching formulae and tableaux --
The Cauchy identity --
Unitary branching rules --
The involution model for Sk --
Some symmetric algebras --
Gelfand pairs --
Hecke algebras --
The philosophy of cusp forms --
Cohomology of Grassmannians. Pt. I: Compact groups. Haar measure --
Schur orthogonality --
Compact operators --
The Peter-Weyl theorem --
pt. II: Lie groups fundamentals. Lie subgroups of GL (n,C) --
Vector fields --
Left-invariant vector fields --
The exponential map --
Tensors and universal properties --
The universal enveloping algebra --
Extension of scalars --
Representations of s1(2,C) --
The universal cover --
The local Frobenius theorem --
Tori --
Geodesics and maximal tori --
Topological proof of Cartan's theorem --
The Weyl integration formula --
The root system --
Examples of root systems --
Abstract Weyl groups --
The fundamental group --
Semisimple compact groups --
Highest-Weight vectors --
The Weyl character formula --
Spin --
Complexification --
Coxeter groups --
The Iwasawa decomposition --
The Bruhat decomposition --
Symmetric spaces --
Relative root systems --
Embeddings of lie groups --
pt. III: Topics. Mackey theory --
Characters of GL(n,C) --
Duality between Sk and GL(n, C) --
The Jacobi-Trudi identity --
Schur polynomials and GL(n,C) --
Schur polynomials and Sk --
Random matrix theory --
Minors of Toeplitz matrices --
Branching formulae and tableaux --
The Cauchy identity --
Unitary branching rules --
The involution model for Sk --
Some symmetric algebras --
Gelfand pairs --
Hecke algebras --
The philosophy of cusp forms --
Cohomology of Grassmannians.
Series Title: Graduate texts in mathematics, 225.
Responsibility: Daniel Bump.
More information:

Abstract:

Going beyond the representation theory of compact Lie groups, this book offers a carefully chosen range of material conveying the bigger picture. Covers Lie algebra, Weyl character formula,  Read more...

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From the reviews of the second edition: "This is a graduate math level text. Concise with lots of proofs. The chapters are short enough to read in one sitting. ... I was asked to look for books on Read more...

 
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schema:description"Pt. I: Compact groups. Haar measure -- Schur orthogonality -- Compact operators -- The Peter-Weyl theorem -- pt. II: Lie groups fundamentals. Lie subgroups of GL (n,C) -- Vector fields -- Left-invariant vector fields -- The exponential map -- Tensors and universal properties -- The universal enveloping algebra -- Extension of scalars -- Representations of s1(2,C) -- The universal cover -- The local Frobenius theorem -- Tori -- Geodesics and maximal tori -- Topological proof of Cartan's theorem -- The Weyl integration formula -- The root system -- Examples of root systems -- Abstract Weyl groups -- The fundamental group -- Semisimple compact groups -- Highest-Weight vectors -- The Weyl character formula -- Spin -- Complexification -- Coxeter groups -- The Iwasawa decomposition -- The Bruhat decomposition -- Symmetric spaces -- Relative root systems -- Embeddings of lie groups -- pt. III: Topics. Mackey theory -- Characters of GL(n,C) -- Duality between Sk and GL(n, C) -- The Jacobi-Trudi identity -- Schur polynomials and GL(n,C) -- Schur polynomials and Sk -- Random matrix theory -- Minors of Toeplitz matrices -- Branching formulae and tableaux -- The Cauchy identity -- Unitary branching rules -- The involution model for Sk -- Some symmetric algebras -- Gelfand pairs -- Hecke algebras -- The philosophy of cusp forms -- Cohomology of Grassmannians."@en
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