Identities Relating Schur s-Functions and Q-Functions.

Abstract

Schur s- and Q-functions are two important families of symmetric functions, with applications for other fields, such as the representation theory of the symmetric group. Other researchers have shown that there are unexpected equalities between seemingly unrelated skew s-functions. In this dissertation we investigate similar relationships among Q-functions and between s- and Q-functions. In particular, we determine which s-functions are a linear combination of Q-functions, showing in addition that all are Q-positive, and determine which s-functions are constant multiples of single non-skew Q-functions. For skew Q-functions whose diagrams are valid unshifted shapes, we determine which ones are constant multiples of single non-skew Q-functions.