Year: 2024
Type: article
Abstract: Let n n be a non-negative integer. Combining algebraic and combinatorial techniques, we investigate for which pairs ( G , ρ ) (G,\rho ) of a subgroup G G of the symmetric group S n S_n and an irreducible character ρ \rho of G G the induced character ρ ↑ S n \rho \!\uparrow ^{S_n} is multiplicity-free. As a result, for n ≥ 66 n\geq 66 , we classify all subgroups G ≤ S n G\leq S_n which give rise to such a pair. Moreover, for the majority of these groups G G we identify all the possible choices of the irreducible character ρ \rho , assuming n ≥ 73 n\geq 73 .
DOI: 10.1090/tran/9295
Author: Pavel Turek
Institution: Royal Holloway University of London
Language: English
Topic: Finite Group Theory Research
Subfield: Discrete Mathematics and Combinatorics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W4403293073