Eugenio Giannelli

Vertices of Simple Modules of Symmetric Groups Labelled by Hook Partitions

Abstract In this article we study the vertices of simple modules for the symmetric groups in prime characteristic p. In particular, we complete the classification of the vertices of simple F𝔖n-modules labelled by hook partitions.

Hausdorff dimension in R-analytic profinite groups

Abstract We study the Hausdorff dimension of R-analytic subgroups in an infinite R-analytic profinite group, where R is a pro-p ring whose associated graded ring is an integral domain. In particular, we prove that the set of such Hausdorff dimensions is a finite subset of the rational numbers.

On signed Young permutation modules and signed p-Kostka numbers

Abstract We prove the existence and main properties of signed Young modules for the symmetric group, using only basic facts about symmetric group representations and the Broué correspondence. We then prove new reduction theorems for the signed p-Kostka numbers, defined to be the multiplicities of signed Young modules as direct summands of signed Young permutation modules. We end by classifying the indecomposable signed Young permutation modules and determining their endomorphism algebras.