Normalized characters of symmetric groups and Boolean cumulants via Khovanov's Heisenberg category
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Journal Title
Journal ISSN
Volume Title
A1 Alkuperäisartikkeli tieteellisessä aikakauslehdessä
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Author
Date
2023-05
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Mcode
Degree programme
Language
en
Pages
Series
Journal of Combinatorial Theory. Series A, Volume 196
Abstract
In this paper, we study relationships between the normalized characters of symmetric groups and the Boolean cumulants of Young diagrams. Specifically, we show that each normalized character is a polynomial of twisted Boolean cumulants with coefficients being non-negative integers, and conversely, that, when we expand a Boolean cumulant in terms of normalized characters, the coefficients are again non-negative integers. The main tool is Khovanov's Heisenberg category and the recently established connection of its center to the ring of functions on Young diagrams, which enables one to apply graphical manipulations to the computation of functions on Young diagrams. Therefore, this paper is an attempt to deepen the connection between the asymptotic representation theory and graphical categorification.Description
Funding Information: This work was supported by Grant-in-Aid for Japan Society for the Promotion of Science Fellows (No. 19J01279 ) and postdoctoral researcher funding from Academy of Finland (No. 248130 ). The author thanks the anonymous referees for helping the author improve the manuscript, especially by pointing out errors in the first submission. Publisher Copyright: © 2023 The Author(s)
Keywords
Boolean cumulants, Heisenberg category, Normalized character, Symmetric group
Citation
Koshida , S 2023 , ' Normalized characters of symmetric groups and Boolean cumulants via Khovanov's Heisenberg category ' , Journal of Combinatorial Theory. Series A , vol. 196 , 105735 . https://doi.org/10.1016/j.jcta.2023.105735
