Download E-books Group Characters, Symmetric Functions, and the Hecke Algebra (University Lecture Series) PDF

By David M. Goldschmidt

Directed at graduate scholars and mathematicians, this ebook covers an strange set of interrelated issues, providing a self-contained exposition of the algebra in the back of the Jones polynomial in addition to quite a few tours into similar components. The publication is made of lecture notes from a path taught by means of Goldschmidt on the collage of California at Berkeley in 1989. The direction was once geared up in 3 elements. half I covers, between different issues, Burnside's Theorem that teams of order $p^aq^b$ are solvable, Frobenius' Theorem at the life of Frobenius kernels, and Brauer's characterization of characters. half II covers the classical personality idea of the symmetric workforce and comprises an set of rules for computing the nature desk of $S^n$; a building of the Specht modules; the 'determinant shape' for the irreducible characters; the hook-length formulation of body, Robinson, and Thrall; and, the Murnaghan-Nakayama formula.Part III covers the standard illustration conception of the Hecke algebra, the development of the two-variable Jones polynomial, and a derivation of Ocneanu's 'weights' as a result of T. A. Springer.

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