Group Characters, Symmetric Functions and the Hecke Algebra
Seiten
1993
American Mathematical Society (Verlag)
978-0-8218-7003-7 (ISBN)
American Mathematical Society (Verlag)
978-0-8218-7003-7 (ISBN)
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Presents an exposition of the algebra behind the Jones polynomial along with various excursions into related areas. This book covers 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.
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.
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.
Part I: Finite-dimensional algebras: Group characters Divisibility Induced characters Further results Part II: Permutations and partitions: The irreducible characters of $S^n$ The Specht modules Symmetric functions The Schur functions The Littlewood-Richardson ring Two useful formulas Part III: The Hecke algebra: The Markov trace.
| Erscheint lt. Verlag | 15.6.1993 |
|---|---|
| Reihe/Serie | University Lecture Series ; No. 4 |
| Verlagsort | Providence |
| Sprache | englisch |
| Maße | 178 x 254 mm |
| Gewicht | 169 g |
| Themenwelt | Mathematik / Informatik ► Mathematik |
| ISBN-10 | 0-8218-7003-3 / 0821870033 |
| ISBN-13 | 978-0-8218-7003-7 / 9780821870037 |
| Zustand | Neuware |
| Informationen gemäß Produktsicherheitsverordnung (GPSR) | |
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