6 papers · 1 filter
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 of a -block of a finite group , then the unit group of contains a basis stabilized by the left and right multiplicative a…
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…
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…
A new canonical induction formula for -permutation modules
Laurence Barker, Hatice Mutlu
Applying Robert Boltje's theory of canonical induction, we give a restriction-preserving formula expressing any -permutation module as a -linear combination of…
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…
Genotypes of irreducible representations of finite p-groups
Laurence Barker
For any characteristic zero coefficient field, an irreducible representation of a finite -group can be assigned a Roquette -group, called the genotype. This has already been…