On the combinatorics of core partitions and applications to the representation theory of the symmetric group.
Lead Research Organisation:
Queen Mary University of London
Department Name: Sch of Mathematical Sciences
Abstract
We will start by attempting to generalise theorems on core-partitions for bar-core partitions. For example, it has been proved for two coprime positive integers s and t that the s-weight of the t-core of a partition is at most the s-weight of the partition itself, and it is also known that if s and t are also both odd then the s-bar-core of a t-bar-core is again a s-bar-core; we will try to show that the 's-bar-weight' of a t-bar-core of a partition is at most the 's-bar-weight' of the original partition.
Later, we will use these generalised theorems to establish results on the representation theory of double-covers of the symmetric group, as there is an intimate correspondence here with the combinatorics of bar-core partitions.
Later, we will use these generalised theorems to establish results on the representation theory of double-covers of the symmetric group, as there is an intimate correspondence here with the combinatorics of bar-core partitions.
People |
ORCID iD |
Matthew Fayers (Primary Supervisor) | |
Dean Yates (Student) |
Studentship Projects
Project Reference | Relationship | Related To | Start | End | Student Name |
---|---|---|---|---|---|
EP/R513106/1 | 01/10/2018 | 30/09/2023 | |||
2104708 | Studentship | EP/R513106/1 | 01/10/2018 | 30/09/2022 | Dean Yates |