A symmetric Bloch-Okounkov theorem

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.

Cited by in corpus (3)

• Partition Eisenstein series and semi-modular forms
• The Bloch-Okounkov theorem for congruence subgroups and Taylor coefficients of quasi-Jacobi forms
• Quantum KdV hierarchy and shifted symmetric functions