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Vanessa's receptions - Group Characters, Symmetric Functions, and the Hecke Algebra download pdf

Vanessa's receptions

Group Characters, Symmetric Functions, and the Hecke Algebra by David M. Goldschmidt

Group Characters, Symmetric Functions, and the Hecke Algebra



Download Group Characters, Symmetric Functions, and the Hecke Algebra




Group Characters, Symmetric Functions, and the Hecke Algebra David M. Goldschmidt
Language: English
Page: 69
Format: pdf
ISBN: 0821870033, 9780821870037
Publisher: American Mathematical Society

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.

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