On the Existence of Elementwise Invariant Vectors in Representations of Symmetric Groups

Abstract

We determine when a permutation with cycle type $\mu$ admits a non-zero invariant vector in the irreducible representation $V_{\lambda }$ of the symmetric group. We find that a majority of pairs $(\lambda ,\mu )$ have this property, with only a few simple exceptions.

16 pages, 11 figures (added citations)