E. Giannelli

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20242026

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math.RT2025

Degrees and prime power order zeros of characters of symmetric and alternating groups

Eugenio Giannelli, Stacey Law, Eoghan McDowell

We show that the $p$ -part of the degree of an irreducible character of a symmetric group is completely determined by the set of vanishing elements of $p$ -power order. As a corollar…

math.GR2025

On the number and sizes of double cosets of Sylow subgroups of the symmetric group

Persi Diaconis, Eugenio Giannelli, Robert M. Guralnick +4

Let $P_{n}$ be a Sylow $p$ -subgroup of the symmetric group $S_{n}$ . We investigate the number and sizes of the $P_{n} ∖ S_{n} / P_{n}$ double cosets, showing that most double cosets…

math.RT2025

Sylow branching trees for symmetric groups

Eugenio Giannelli, Stacey Law

Let $p \geq 5$ be a prime and let $P$ be a Sylow $p$ -subgroup of a finite symmetric group. To every irreducible character of $P$ we associate a collection of labelled, complete $p$ -a…