Year: 2025
Type: article
Abstract: We consider problems concerning the largest degrees of irreducible characters of symmetric groups, and the multiplicities of character degrees of symmetric groups. Using evidence from computer experiments, we posit several new conjectures or extensions of previous conjectures, and prove a number of results. One of these is that, if n≥21, then there are at least eight irreducible characters of Sn, all of which have the same degree, and which have irreducible restriction to An. We explore similar questions about unipotent degrees of GLn(q). We also make some remarks about how the experiments here shed light on posited algorithms for finding the largest irreducible character degree of Sn.
Source: Experimental Mathematics
Author: David A. Craven
Institution: University of Birmingham
Language: English
Topic: Finite Group Theory Research
Subfield: Discrete Mathematics and Combinatorics
Field: Mathematics
Domain: Physical Sciences
Open Access status: hybrid
OpenAlex ID: W4410617992