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arXiv · 2509.12904

Asymptotics of higher Lie characters

Ron M. Adin·Yuval Roichman·Natalia Tsilevich
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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.

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Ron M. Adin, Yuval Roichman, Natalia Tsilevich. 2025-09-16. Asymptotics of higher Lie characters. https://arxiv.org/abs/2509.12904

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