A symmetric Bloch-Okounkov theorem

The algebra of so-called shifted symmetric functions on partitions has the property that for all elements a certain generating series, called the \(q\)-bracket, is a quasimodular form. More generally, if a graded algebra \(A\) of functions on partitions has the property that the \(q\)-bracket of eve...

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Bibliographic Details
Published in:arXiv.org 2021-03
Main Author: van Ittersum, Jan-Willem M
Format: Article
Language:English
Subjects:
Algebra
Mathematical analysis
Partitions
Polynomials
Online Access:Get full text
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Summary:The algebra of so-called shifted symmetric functions on partitions has the property that for all elements a certain generating series, called the \(q\)-bracket, is a quasimodular form. More generally, if a graded algebra \(A\) of functions on partitions has the property that the \(q\)-bracket of every element is a quasimodular form of the same weight, we call \(A\) a quasimodular algebra. We introduce a new quasimodular algebra consisting of symmetric polynomials in the part sizes and multiplicities.
ISSN:2331-8422
DOI:10.48550/arxiv.2006.03401