Basic Orders for Defect Two Blocks of $\Z_p\Sym_n$

TL;DR

This paper presents a combinatorial method for constructing basic orders for defect two blocks of symmetric groups over p-adic integers, advancing the understanding of their algebraic structure.

Contribution

It introduces a new combinatorial approach to explicitly construct basic orders for defect two blocks of symmetric groups over p-adic integers.

Findings

Explicit combinatorial construction of basic orders

Enhanced understanding of defect two block structures

Potential applications to modular representation theory

Abstract

We show how basic orders for defect two blocks of symmetric groups over the ring of $p$-adic integers can be constructed by purely combinatorial means.