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arXiv · 2308.08146

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

Amrutha P·Amritanshu Prasad·Velmurugan S
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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.

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Amrutha P, Amritanshu Prasad, Velmurugan S. 2023-08-16. On the Existence of Elementwise Invariant Vectors in Representations of Symmetric Groups. https://arxiv.org/abs/2308.08146

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