# Uglov bipartitions and extended Young diagrams

## TL;DR

This paper investigates Uglov bipartitions, generalizes a conjecture, and explores implications for canonical bases and decomposition matrices in affine type A and type Bn Hecke algebras.

## Contribution

It introduces a broader understanding of Uglov bipartitions and extends a key conjecture, impacting computations in affine type A and Hecke algebra representations.

## Key findings

- Generalization of a conjecture by Dipper, James, and Murphy
- Enhanced methods for computing canonical bases in affine type A
- New description of decomposition matrices for Hecke algebras of type Bn

## Abstract

We study the class of Uglov bipartitions and prove a generalization of a conjecture by Dipper, James and Murphy. We give two consequences concerning the computation of canonical bases in affine type A and the description of decomposition matrices for Hecke algebras of type Bn in arbitrary characteristic.