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arXiv · 2006.03401

A symmetric Bloch-Okounkov theorem

Jan-Willem M. van Ittersum
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Abstract

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.

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Jan-Willem M. van Ittersum. 2020-06-05. A symmetric Bloch-Okounkov theorem. https://doi.org/10.1007/s40687-021-00253-8

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