Abstract

We provide an expository overview of shifted symmetric functions by focusing on their evaluation on Young diagrams and their expression in multirectangular coordinates. Shifted Schur functions are shown to be polynomials in these coordinates, with nonnegative coeffecients when expanded in the falling factorial basis. Motivated by classical results on symmetric functions, we then explore relations and generalizations to Jack polynomials. This paper surveys the work of Alexandersson and Féray (2017) and the frameworks provided by Stanley (2001, 2002) and Okounkov-Olshanski (1997a, 1997b).