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.
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.
Organisations
People |
ORCID iD |
| Corneliu Hoffman (Primary Supervisor) | |
| Mark Butler (Student) |
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 | 02/10/2017 | 31/03/2021 | Mark 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. |