9780821870037
Group Characters, Symmetric Functions, And The Hecke Algebra (University Lecture Series) - David M. Goldschmidt
American Mathematical Society (1993)
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#4089

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Hecke algebras, Representations of groups, Finite groups

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.

Product Details
LoC Classification QA174.2 .G65 1993
Dewey 512.2
Format Paperback
Cover Price 18,00 €
No. of Pages 73
Height x Width 246 x 173 mm
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