MARC details
| 000 -LEADER |
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| fixed length control field |
03835cam a22003617i 4500 |
| 001 - CONTROL NUMBER |
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| control field |
17800166 |
| 003 - CONTROL NUMBER IDENTIFIER |
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| control field |
OSt |
| 005 - DATE AND TIME OF LATEST TRANSACTION |
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| control field |
20160617143033.0 |
| 008 - FIXED-LENGTH DATA ELEMENTS--GENERAL INFORMATION |
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| fixed length control field |
130703t20132013nyua b 001 0 eng d |
| 010 ## - LIBRARY OF CONGRESS CONTROL NUMBER |
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| LC control number |
2013944369 |
| 020 ## - INTERNATIONAL STANDARD BOOK NUMBER |
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| International Standard Book Number |
9788181284495 |
| 035 ## - SYSTEM CONTROL NUMBER |
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| System control number |
(OCoLC)ocn861337404 |
| 040 ## - CATALOGING SOURCE |
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| Original cataloging agency |
IISER Bhopal |
| Language of cataloging |
eng |
| Transcribing agency |
VBD |
| 042 ## - AUTHENTICATION CODE |
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| Authentication code |
lccopycat |
| 050 00 - LIBRARY OF CONGRESS CALL NUMBER |
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| Classification number |
QA387 |
| Item number |
.B76 2013 |
| 082 00 - DEWEY DECIMAL CLASSIFICATION NUMBER |
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| Classification number |
512.482 B88L |
| Edition number |
23 |
| 100 1# - MAIN ENTRY--PERSONAL NAME |
|---|
| Personal name |
Bump, Daniel. |
| 9 (RLIN) |
6141 |
| 222 ## - KEY TITLE |
|---|
| Key title |
Mathematics Collection |
| 245 10 - TITLE STATEMENT |
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| Title |
Lie groups |
| Statement of responsibility, etc |
Daniel Bump. |
| 260 ## - PUBLICATION, DISTRIBUTION, ETC. (IMPRINT) |
|---|
| Place of publication, distribution, etc |
New Delhi : |
| Name of publisher, distributor, etc |
Springer, |
| Date of publication, distribution, etc |
2004. |
| 300 ## - PHYSICAL DESCRIPTION |
|---|
| Extent |
xiii, 551 p. : |
| Other physical details |
ill. ; |
| Dimensions |
25 cm. |
| 440 ## - SERIES STATEMENT/ADDED ENTRY--TITLE |
|---|
| Title |
Graduate text in mathematics; |
| Number of part/section of a work |
225 |
| 9 (RLIN) |
9646 |
| 504 ## - BIBLIOGRAPHY, ETC. NOTE |
|---|
| Bibliography, etc |
Includes bibliographical references (pages 535-544) and index. |
| 505 00 - FORMATTED CONTENTS NOTE |
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| Miscellaneous information |
Pt. I: |
| Title |
Compact groups. |
| -- |
Haar measure -- |
| -- |
Schur orthogonality -- |
| -- |
Compact operators -- |
| -- |
The Peter-Weyl theorem -- |
| Miscellaneous information |
pt. II: |
| Title |
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 -- |
| Miscellaneous information |
pt. III: |
| Title |
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. |
| 520 ## - SUMMARY, ETC. |
|---|
| Summary, etc |
"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. The book continues with the study of complex analytic groups, then general noncompact Lie groups, including the Coxeter presentation of the Weyl group, the Iwasawa and Bruhat decompositions, Cartan decomposition, symmetric spaces, Cayley transforms, relative root systems, Satake diagrams, extended Dynkin diagrams and a survey of the ways Lie groups may be embedded in one another. The book culminates in a "topics" section giving depth to the student's understanding of representation theory, taking the Frobenius-Schur duality between the representation theory of the symmetric group and the unitary groups as a unifying theme, with many applications in diverse areas such as random matrix theory, minors of Toeplitz matrices, symmetric algebra decompositions, Gelfand pairs, Hecke algebras, representations of finite general linear groups and the cohomology of Grassmannians and flag varieties.-- |
| 650 #0 - SUBJECT ADDED ENTRY--TOPICAL TERM |
|---|
| Topical term or geographic name as entry element |
Lie groups. |
| 9 (RLIN) |
6142 |
| 650 #0 - SUBJECT ADDED ENTRY--TOPICAL TERM |
|---|
| Topical term or geographic name as entry element |
Mathematics. |
| 9 (RLIN) |
6143 |
| 830 #0 - SERIES ADDED ENTRY--UNIFORM TITLE |
|---|
| Uniform title |
Graduate texts in mathematics ; |
| Volume number/sequential designation |
225. |
| 9 (RLIN) |
6144 |
| 906 ## - LOCAL DATA ELEMENT F, LDF (RLIN) |
|---|
| a |
7 |
| b |
cbc |
| c |
copycat |
| d |
2 |
| e |
ncip |
| f |
20 |
| g |
y-gencatlg |
| 942 ## - ADDED ENTRY ELEMENTS (KOHA) |
|---|
| Source of classification or shelving scheme |
Dewey Decimal Classification |
| Koha item type |
Books |
