Symmetric and non-symmetric Jack Functions

Abstract

The goal of this dissertation is to present the theory of Jack functions from the standpoint of algebraic combinatorics. The presentation of symmetric functions is largely centred on the first chapter of MacDonald's "Symmetric Functions and Hall's Polynomials" [7]. Symmetric and non-symmetric Jack functions are characterized by Sahi-Knop's [4] combinatorial formulas. Moreover, Stanley's Pieri-type rule [15] for symmetric Jack functions and Schützer's [13] Pieri-type rule for non-symmetric functions are thoroughly described.