Electronic Resource

Lie groups

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This book is intended for a one-year graduate course on Lie groups and Lie algebras. The book goes 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. The book is organized to allow different paths through the material depending on one's interests. This second edition has substantial new material, including improved discussions of underlying principles, streamlining of some proofs, and many results and topics that were not in the first edition.
For compact Lie groups, the book covers the Peter–Weyl theorem, Lie algebra, conjugacy of maximal tori, the Weyl group, roots and weights, Weyl character formula, the fundamental group and more. The book continues with the study of complex analytic groups and general noncompact Lie groups, covering the Bruhat decomposition, Coxeter groups, flag varieties, symmetric spaces, Satake diagrams, embeddings of Lie groups and spin. Other topics that are treated are symmetric function theory, the representation theory of the symmetric group, Frobenius–Schur duality and GL(n) × GL(m) duality with many applications including some in random matrix theory, branching rules, Toeplitz determinants, combinatorics of tableaux, Gelfand pairs, Hecke algebras, the "philosophy of cusp forms" and the cohomology of Grassmannians. An appendix introduces the reader to the use of Sage mathematical software for Lie group computations.

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Ketersediaan

Informasi Detail

Judul Seri

Graduate texts in mathematics

No. Panggil

E622

Penerbit

New York : Springer., 2013

Deskripsi Fisik

xiii, 551 hlm.

Bahasa

English

ISBN/ISSN

9781461480242

Klasifikasi

NONE

Tipe Isi

text

Tipe Media

computer

Tipe Pembawa

online resource

Edisi

2

Subjek

Aljabar Linear

Info Detail Spesifik

-

Pernyataan Tanggungjawab

Daniel Bump

Versi lain/terkait

Lampiran Berkas

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