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## Details

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:

## Reviews

*Editorial reviews*

Publisher Synopsis

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 this topic. It was challenging to search for material with this title. This was the best book that I could find. I look forward to exploring this topic further." (Mary Anne, Cats and Dogs with Data, maryannedata.com, April, 2014) "The book begins with a detailed explanation of the basic facts. ... It contains a discussion of very nontrivial modern applications of Lie group theory in other areas of mathematics. ... The text is very interesting and is superior to other textbooks on Lie group theory." (Dmitri Artamonov, zbMATH, Vol. 1279, 2014) "This second edition of a successful graduate textbook and reference is now divided in four parts. ... the book under review is the one every one of us must have on its desk or night table. ... this is a well-organized book with clear and well-established goals, taking the interested reader to the frontiers of today's research." (Felipe Zaldivar, MAA Reviews, December, 2013) Read more...

*User-contributed reviews*