V. S.

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math.RT2024

On Minimal Polynomials of Elements in Symmetric and Alternating Groups

Velmurugan S

Let $(ρ, V)$ be an irreducible representation of the symmetric group $S_{n}$ (or the alternating group $A_{n}$ ), and let $g$ be a permutation on $n$ letters with each of its cycl…

math.RT2024

Cyclic Characters of Alternating Groups

Amrutha P, Amritanshu Prasad, Velmurugan S

We determine the eigenvalues with multiplicity of each element of an alternating group in any irreducible representation. This is equivalent to determining the decomposition of cyc…

math.RT2023

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

Amrutha P, Amritanshu Prasad, Velmurugan S

We determine when a permutation with cycle type $μ$ admits a non-zero invariant vector in the irreducible representation $V_{λ}$ of the symmetric group. We find that a majority of pa…