The plethystic inverse of the odd Lie representations

DOI10.1090/proc/15938zbMath1492.05161arXiv2003.10700OpenAlexW4200202045MaRDI QIDQ5086926

Sheila Sundaram

Publication date: 8 July 2022

Published in: Proceedings of the American Mathematical Society (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/2003.10700

zbMATH Keywords

free Lie algebraplethysmplethysric inverseSchur \(p\)-functions

Mathematics Subject Classification ID

Exact enumeration problems, generating functions (05A15) Symmetric functions and generalizations (05E05) Combinatorial aspects of representation theory (05E10) Representations of finite symmetric groups (20C30) Group rings of finite groups and their modules (group-theoretic aspects) (20C05)

Cites Work

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• Alternating permutations and symmetric functions
• Enumeration of permutations with prescribed up-down and inversion sequences
• The conjugacy action of \(S_n\) and modules induced from centralisers
• Staircase skew Schur functions are Schur \(P\)-positive
• On a curious variant of the \(S_n\)-module \(\text{Lie}_n\)
• Enumeration of up-down sequences
• Representations of the Symmetric Group in Deformations of the Free Lie Algebra
• On Symmetrized Kronecker Powers and the Structure of the Free Lie Ring

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