Séminaire Lotharingien de Combinatoire, 95B.27 (2026), 12 pp.
Ron M. Adin, Yuval Roichman and Natalia Tsilevich
Asymptotics of Higher Lie Characters (Extended Abstract)
Abstract.
Higher Lie characters form a distinguished family of symmetric group
characters, which appear in many areas of algebra and
combinatorics. An old open problem of Thrall is to decompose them into
irreducibles.
We propose a novel asymptotic approach to this problem, showing
that many families of higher Lie characters
tend to be proportional to the regular character.
In particular, a random higher Lie character
tends, in probability, to be proportional to the regular character.
Received: November 15, 2025.
Accepted: February 15, 2026.
Final version: April 1, 2026.
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