Skip to Main Content

Proceedings of the American Mathematical Society

Published by the American Mathematical Society since 1950, Proceedings of the American Mathematical Society is devoted to shorter research articles in all areas of pure and applied mathematics.

ISSN 1088-6826 (online) ISSN 0002-9939 (print)

The 2024 MCQ for Proceedings of the American Mathematical Society is 0.85.

What is MCQ? The Mathematical Citation Quotient (MCQ) measures journal impact by looking at citations over a five-year period. Subscribers to MathSciNet may click through for more detailed information.

 

The plethystic inverse of the odd Lie representations
HTML articles powered by AMS MathViewer

by Sheila Sundaram
Proc. Amer. Math. Soc. 150 (2022), 3787-3798
DOI: https://doi.org/10.1090/proc/15938
Published electronically: April 29, 2022

Abstract:

The Frobenius characteristic of $Lie_n$, the representation of the symmetric group $S_n$ afforded by the multilinear part of the free Lie algebra, is known to satisfy many interesting plethystic identities. In this paper we prove a conjecture of Richard Stanley establishing the plethystic inverse of the sum $\sum _{n\geq 0} Lie_{2n+1}$ of the odd Lie characteristics. We obtain an apparently new plethystic decomposition of the regular representation of $S_n$ in terms of irreducibles indexed by hooks, and the Lie representations. We also determine the plethystic inverse of the alternating sum of the odd Lie characteristics.
References
Similar Articles
  • Retrieve articles in Proceedings of the American Mathematical Society with MSC (2020): 05E10, 20C30
  • Retrieve articles in all journals with MSC (2020): 05E10, 20C30
Bibliographic Information
  • Sheila Sundaram
  • Affiliation: Pierrepont School, One Sylvan Road North, Westport, Connecticut 06880
  • MR Author ID: 271955
  • ORCID: 0000-0002-1583-4740
  • Email: shsund@comcast.net
  • Received by editor(s): March 25, 2021
  • Received by editor(s) in revised form: December 8, 2021
  • Published electronically: April 29, 2022

  • Dedicated: In memory of my mother, Nirmala Sundaram
  • Communicated by: Patricia L. Hersh
  • © Copyright 2022 American Mathematical Society
  • Journal: Proc. Amer. Math. Soc. 150 (2022), 3787-3798
  • MSC (2020): Primary 05E10, 20C30
  • DOI: https://doi.org/10.1090/proc/15938
  • MathSciNet review: 4446229