Laurence Barker

activity

20182023

collaborators

9 papers

math.RT2023

Pointed fusion systems of blocks

Laurence Barker

The pointed fusion system of a block is a structure consisting of the fusions and relative multiplicities between the local pointed groups associated with a maximal Brauer pair. We…

math.RT2023

The pointed $p$ -groups on a block algebra

Laurence Barker

A pointed $p$ -group is a pointed group $P_{γ}$ such that $P$ is a $p$ -group. We parameterize the pointed $p$ -groups on a group algebra or on a block algebra of a group algebra. The p…

math.RT2021

Conjectural invariance with respect to the fusion system of an almost-source algebra

Laurence Barker, Matthew Gelvin

We show that, given an almost-source algebra $A$ of a $p$ -block of a finite group $G$ , then the unit group of $A$ contains a basis stabilized by the left and right multiplicative a…

math.RT2020

Semisimplicity of some deformations of the subgroup category and the biset category

Laurence Barker, İsmail Alperen Öğüt

We introduce some deformations of the biset category and prove a semisimplicity property. We also consider another group category, called the subgroup category, whose morphisms are…

math.RT2020

Some deformations of the fibred biset category

Laurence Barker, İsmail Alperen Öğüt

We prove the well-definedness of some deformations of the fibred biset category in characteristic zero. The method is to realize the fibred biset category and the deformations as t…

math.RT2019

Variants on a conjecture relating block source algebras to characteristic bisets

Laurence Barker, Matthew Gelvin

Given a block of a finite group, any source algebra has a basis invariant under the multiplicative actions of the defect group. Is such a basis a characteristic biset of the block…

math.RT2018

A new canonical induction formula for $p$ -permutation modules

Laurence Barker, Hatice Mutlu

Applying Robert Boltje's theory of canonical induction, we give a restriction-preserving formula expressing any $p$ -permutation module as a $Z [1/ p]$ -linear combination of…

math.RT2018

An inversion formula for the primitive idempotents of the trivial source algebra

Laurence Barker

Formulas for the primitive idempotents of the trivial source algebra, in characteristic zero, have been given by Boltje and Bouc--Thévenaz. We shall give another formula for those…

math.RT2018

Genotypes of irreducible representations of finite p-groups

Laurence Barker

For any characteristic zero coefficient field, an irreducible representation of a finite $p$ -group can be assigned a Roquette $p$ -group, called the genotype. This has already been…

Pointed fusion systems of blocks

The pointed p-groups on a block algebra

Conjectural invariance with respect to the fusion system of an almost-source algebra

Semisimplicity of some deformations of the subgroup category and the biset category

Some deformations of the fibred biset category

Variants on a conjecture relating block source algebras to characteristic bisets

A new canonical induction formula for p-permutation modules

An inversion formula for the primitive idempotents of the trivial source algebra

Genotypes of irreducible representations of finite p-groups

The pointed $p$ -groups on a block algebra

A new canonical induction formula for $p$ -permutation modules