Applying amalgams to representation theory and cohomology

Lead Research Organisation: University of Birmingham
Department Name: School of Mathematics

Abstract

The project is in Pure Mathematics/Algebra, more precisely in the area of finite groups ant their representations.

In a series of papers Ronan and Smith introduced a generalisation of induction and restriction from representation theory to similar concepts on amalgams of groups. The project proposes to specialise these methods to specific amalgam presentation of Coxeter groups and groups of of Lie type and use them to compute their representations and cohomology.

Publications

10 25 50

Studentship Projects

Project Reference Relationship Related To Start End Student Name
EP/N509590/1 01/10/2016 30/09/2021
1935781 Studentship EP/N509590/1 25/09/2017 24/09/2021 Mark William Butler
 
Title Magma program to enumerate subsheaves of the constant sheaf on the building of $S_n$ 
Description Code written in the computer algebra system Magma which constructs the Tits building $\Delta$ for the permutation group $G = S_n$, for small values of $n$, then takes as input a $G$-module $V$ and enumerates all subsheaves of the constant sheaf $\mathscr{F}_V$ on $\Delta$. 
Type Of Technology Software 
Year Produced 2018 
Impact This has given some insight into which combinations of module choices are possible on these sheaves.