On problems in the representation theory of symmetric groups

SWC Law - 2020 - repository.cam.ac.uk
In this thesis, we study the representation theory of the symmetric groups S n, their Sylow p-
subgroups P n and related algebras. For all primes p and natural numbers n, we determine …

On the Aα-Spectral Radii of Cactus Graphs

C Wang, S Wang, JB Liu, B Wei - Mathematics, 2020 - mdpi.com
Let A (G) be the adjacent matrix and D (G) the diagonal matrix of the degrees of a graph G,
respectively. For 0≤ α≤ 1, the A α-matrix is the general adjacency and signless Laplacian …

Macdonald trees and determinants of representations for finite Coxeter groups

A Ayyer, A Prasad, S Spallone - arXiv preprint arXiv:1812.00608, 2018 - arxiv.org
Every irreducible odd dimensional representation of the $ n $'th symmetric or
hyperoctahedral group, when restricted to the $(n-1) $'th, has a unique irreducible odd …

Hook removal operators on the odd Young graph

C Bessenrodt, E Giannelli, JB Olsson - Algebraic Combinatorics, 2019 - numdam.org
In this article we consider hook removal operators on odd partitions, ie, partitions labelling
odd-degree irreducible characters of finite symmetric groups. In particular we complete the …