Morita Equivalent Blocks of Symmetric Groups

TL;DR

This paper investigates the lower bounds on the number of Morita equivalence classes of p-blocks of symmetric groups with a fixed weight, expanding understanding of their classification.

Contribution

It provides a new lower bound on the count of Morita equivalence classes for symmetric group blocks with a given weight.

Findings

Establishes a lower bound on Morita equivalence classes

Enhances classification understanding of symmetric group blocks

Builds on Scopes' finiteness result

Abstract

A well-known result of Scopes states that there are only finitely many Morita equivalence classes of $p$-blocks of symmetric groups with a given weight (or defect). In this note we investigate a lower bound on the number of those Morita equivalence classes.