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Multiplicity-free induced characters of symmetric groups

Pavel Turek

Royal Holloway, University of London

Time: 16:00-17:00 (GMT+8), Wednesday May 14th, 2025
Location: Zoom

Abstract: Let \(n\) be a sufficiently large positive integer. A character is multiplicity-free if its irreducible constituents appear with multiplicity one. Wildon in 2009 and independently Godsil and Meagher in 2010 have found all multiplicity-free permutation characters of the symmetric group \(S_n\). In this talk, we focus on a significantly more general problem when the permutation characters are replaced by induced characters of the form \(\rho\!\uparrow^{S_n}\) with \(\rho\) irreducible.             

Despite the nature of the problem, I explain, combining results from group theory, representation theory and combinatorics, why this problem may be feasible and present a close to full answer. I also mention some of my (often surprising) results to questions about conjugate partitions, which naturally arise when solving the problem, and the remarkable complete classification of subgroups \(G\) of \(S_n\), which have an irreducible character which stays multiplicity-free when induced to \(S_n\).

Host: 张宝羽 Baoyu Zhang