eBook ISBN:  9780821832202 
Product Code:  ULECT/4.E 
List Price:  $65.00 
MAA Member Price:  $58.50 
AMS Member Price:  $52.00 
eBook ISBN:  9780821832202 
Product Code:  ULECT/4.E 
List Price:  $65.00 
MAA Member Price:  $58.50 
AMS Member Price:  $52.00 

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 selfcontained 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 hooklength formula of Frame, Robinson, and Thrall; and the MurnaghanNakayama formula. Part III covers the ordinary representation theory of the Hecke algebra, the construction of the twovariable Jones polynomial, and a derivation of Ocneanu's “weights” due to T. A. Springer.
ReadershipGraduate students and research mathematicians.

Table of Contents

Chapters

Chapter 1. Finitedimensional 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 $S^n$

Chapter 8. The Specht modules

Chapter 9. Symmetric functions

Chapter 10. The Schur functions

Chapter 11. The LittlewoodRichardson ring

Chapter 12. Two useful formulas

Chapter 13. The Hecke algebra

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 selfcontained 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 hooklength formula of Frame, Robinson, and Thrall; and the MurnaghanNakayama formula. Part III covers the ordinary representation theory of the Hecke algebra, the construction of the twovariable Jones polynomial, and a derivation of Ocneanu's “weights” due to T. A. Springer.
Graduate students and research mathematicians.

Chapters

Chapter 1. Finitedimensional 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 $S^n$

Chapter 8. The Specht modules

Chapter 9. Symmetric functions

Chapter 10. The Schur functions

Chapter 11. The LittlewoodRichardson ring

Chapter 12. Two useful formulas

Chapter 13. The Hecke algebra

Chapter 14. The Markov trace