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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 μ\mu admits a non-zero invariant vector in the irreducible representation VλV_\lambda of the symmetric group. We find that a majority of pairs (λ,μ)(\lambda,\mu) have this property, with only a few simple exceptions.

Keywords

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)