S. Velmurugan

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math.RT2025

Vanishing pairs of conjugacy classes for the symmetric group

Velmurugan S

In this short note, we classify pairs of conjugacy classes of the symmetric group such that any non-linear irreducible character of the symmetric group vanishes on at least one of…

math.RT2024

Covering Numbers of Some Irreducible Characters of the Symmetric Group

Rijubrata Kundu, Velmurugan S

The covering number of a non-linear character $χ$ of a finite group $G$ is the least positive integer $k$ such that every irreducible character of $G$ occurs in $χ^{k}$ . We determine…

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…