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 e-book covers an strange set of interrelated themes, featuring a self-contained exposition of the algebra at the back of the Jones polynomial in addition to quite a few tours into similar parts. The e-book is made of lecture notes from a direction taught via Goldschmidt on the collage of California at Berkeley in 1989. The direction used to be geared up in 3 components. 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 thought of the symmetric staff and contains an set of rules for computing the nature desk of $S^n$; a development 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' because of T. A. Springer.

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