On the Brauer constructions and generic Jordan types of Young modules

TL;DR

This paper investigates the dimensions of Brauer constructions of Young modules in symmetric groups, revealing their dependence on partitions and p-subgroup actions, with explicit calculations for two-part partitions.

Contribution

It provides new formulas and explicit calculations for Brauer constructions and generic Jordan types of Young modules, especially for two-part partitions.

Findings

Dimensions depend only on partitions and p-subgroup orbits.

Reductive formulas are established for these dimensions.

Explicit calculations are performed for two-part partitions.

Abstract

Let p be a prime number. We study the dimensions of Brauer constructions of Young and Young permutation modules with respect to p-subgroups of the symmetric groups. They depend only on partitions labelling the modules and the orbits of the action of the p-subgroups, and are related to their generic Jordan types. We obtain some reductive formulae and, in the case of two-part partitions, make some explicit calculation.