On the Existence of Elementwise Invariant Vectors in Representations of Symmetric Groups
Representation Theory
2023-10-31 v2 Combinatorics
Abstract
We determine when a permutation with cycle type admits a non-zero invariant vector in the irreducible representation of the symmetric group. We find that a majority of pairs have this property, with only a few simple exceptions.
Cite
@article{arxiv.2308.08146,
title = {On the Existence of Elementwise Invariant Vectors in Representations of Symmetric Groups},
author = {Amrutha P and Amritanshu Prasad and Velmurugan S},
journal= {arXiv preprint arXiv:2308.08146},
year = {2023}
}
Comments
16 pages, 11 figures (added citations)