
eBook ISBN: | 978-0-8218-3220-2 |
Product Code: | ULECT/4.E |
List Price: | $65.00 |
MAA Member Price: | $58.50 |
AMS Member Price: | $52.00 |

eBook ISBN: | 978-0-8218-3220-2 |
Product Code: | ULECT/4.E |
List Price: | $65.00 |
MAA Member Price: | $58.50 |
AMS Member Price: | $52.00 |
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Book DetailsUniversity Lecture SeriesVolume: 4; 1993; 73 ppMSC: Primary 20; 57
Directed at graduate students and mathematicians, this book covers an unusual set of interrelated topics, presenting a self-contained exposition of the algebra behind the Jones polynomial along with various excursions into related areas. The book is made up of lecture notes from a course taught by Goldschmidt at the University of California at Berkeley in 1989. The course was organized in three parts. Part I covers, among other things, Burnside's Theorem that groups of order \(p^aq^b\) are solvable, Frobenius' Theorem on the existence of Frobenius kernels, and Brauer's characterization of characters. Part II covers the classical character theory of the symmetric group and includes an algorithm for computing the character table of \(S^n\) ; a construction of the Specht modules; the “determinant form” for the irreducible characters; the hook-length formula of Frame, Robinson, and Thrall; and the Murnaghan-Nakayama formula. Part III covers the ordinary representation theory of the Hecke algebra, the construction of the two-variable Jones polynomial, and a derivation of Ocneanu's “weights” due to T. A. Springer.
ReadershipGraduate students and research mathematicians.
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Table of Contents
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Chapters
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Chapter 1. Finite-dimensional algebras
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Chapter 2. Group characters
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Chapter 3. Divisibility
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Chapter 4. Induced characters
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Chapter 5. Further results
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Chapter 6. Permutations and partitions
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Chapter 7. The irreducible characters of $S^n$
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Chapter 8. The Specht modules
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Chapter 9. Symmetric functions
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Chapter 10. The Schur functions
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Chapter 11. The Littlewood-Richardson ring
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Chapter 12. Two useful formulas
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Chapter 13. The Hecke algebra
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Chapter 14. The Markov trace
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Directed at graduate students and mathematicians, this book covers an unusual set of interrelated topics, presenting a self-contained exposition of the algebra behind the Jones polynomial along with various excursions into related areas. The book is made up of lecture notes from a course taught by Goldschmidt at the University of California at Berkeley in 1989. The course was organized in three parts. Part I covers, among other things, Burnside's Theorem that groups of order \(p^aq^b\) are solvable, Frobenius' Theorem on the existence of Frobenius kernels, and Brauer's characterization of characters. Part II covers the classical character theory of the symmetric group and includes an algorithm for computing the character table of \(S^n\) ; a construction of the Specht modules; the “determinant form” for the irreducible characters; the hook-length formula of Frame, Robinson, and Thrall; and the Murnaghan-Nakayama formula. Part III covers the ordinary representation theory of the Hecke algebra, the construction of the two-variable Jones polynomial, and a derivation of Ocneanu's “weights” due to T. A. Springer.
Graduate students and research mathematicians.
-
Chapters
-
Chapter 1. Finite-dimensional algebras
-
Chapter 2. Group characters
-
Chapter 3. Divisibility
-
Chapter 4. Induced characters
-
Chapter 5. Further results
-
Chapter 6. Permutations and partitions
-
Chapter 7. The irreducible characters of $S^n$
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Chapter 8. The Specht modules
-
Chapter 9. Symmetric functions
-
Chapter 10. The Schur functions
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Chapter 11. The Littlewood-Richardson ring
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Chapter 12. Two useful formulas
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Chapter 13. The Hecke algebra
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Chapter 14. The Markov trace