| Title:
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LIE GROUPS
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| By: |
Daniel Bump |
| Format: |
Hardback |
| List price:
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£74.99 |
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| ISBN 10: |
146148023X |
| ISBN 13: |
9781461480235 |
| Publisher: |
SPRINGER-VERLAG NEW YORK INC. |
| Pub. date: |
1 October, 2013 |
| Edition: |
2nd Revised edition |
| Series: |
Graduate Texts in Mathematics 225 |
| Pages: |
551 |
| Description: |
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, symmetrical function theory, Satake diagrams, Sage software and more. |
| Synopsis: |
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) x 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. |
| Illustrations: |
90 black & white illustrations, biography |
| Publication: |
US |
| Imprint: |
Springer-Verlag New York Inc. |
| Returns: |
Returnable |
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