Equality of Schur and Skew Schur Functions

Abstract

Abstract.We determine the precise conditions under which any skew Schur function is equal to a Schur function over both infinitely and finitely many variables.

Equality of Schur’s Q-functions and Their Skew Analogues

“…In particular, one should mention Stembridge's recent classification of multiplicity-free products of Schur functions [4] which was generalized to P-functions in [2]. The related questions as to when two ribbon Schur functions are equal and when a Schur function is equal to a skew Schur function were answered in [1] and [5]. Here we show that the latter problem has a simple answer for Schur's Q-functions as well.…”

Multiplicity-free Kronecker products of characters of the symmetric groups

“…In the middle picture, the skew diagram ρ/σ decomposes into two pieces δ and δ . Before we state the classification of the basic skew diagrams labelling multiplicity-free skew characters, we recall that the character associated to a skew diagram is homogeneous if and only if the diagram is a partition diagram up to a possible rotation by 180 • ; in which case it is already irreducible (see [BK99,Will05]). Thus, the skew diagram is proper if and only if the corresponding skew character is proper, i.e., it has at least two different constituents.…”

A Hopf Algebraic Approach to Schur Function Identities

“…One question is whether the restrictions on β can be lessened. The simplicity of the key ribbons depends 13 on the special shape of β. The difficulty in generalizing is in finding an appropriate generalization of Lemma 4.7; once we go beyond key ribbons, there can be more than one shape of the same size that can be taken out.…”