Multiplicity-free induced characters of symmetric groups

2023/09/14 by Pavel Turek, Turek, Pavel · 1 citation
Computer Science · Mathematics · #05E05 #20B35 #20C15 (Secondary) #20C30 (Primary) #Coding theory and cryptography #Combinatorics (math.CO) #FOS: Mathematics #Finite Group Theory Research #Limits and Structures in Graph Theory #Representation Theory (math.RT)

paper · pdf · doi:10.48550/arxiv.2309.07761

openalex publication_date 2023/09/14 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Let n be a non-negative integer. Combining algebraic and combinatorial techniques, we investigate for which pairs (G,ρ) of a subgroup G of the symmetric group S_n and an irreducible character ρ of G the induced character ρ \uparrow^S_n is multiplicity-free. As a result, for n≥ 66, we classify all subgroups G≤ S_n which give rise to such a pair. Moreover, for the majority of these groups G we identify all the possible choices of the irreducible character ρ, assuming n≥ 73.

Cited by

• Multiplicity free induction for the pairs (GL₂\timesGL₂,diag(GL₂)) and (SL₃,GL₂) over finite fields

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