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Harmonic shifted symmetric polynomials and the Bloch-Okounkov theorem

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Jan-Willem van Ittersum
Utrecht University
Thu, 2018-09-06 12:05 - 12:25
MPIM Lecture Hall

The Bloch-Okounkov theorem yields a $\eufm{sl}_2$-equivariant map defined by sums over partitions from shifted symmetric polynomials to quasimodular forms. Classical modular forms are precisely given by the kernel of one of the operators of this $\eufm{sl}_2$-triple on quasimodular forms. The inverse image of modular forms, which is the kernel of another operator $\Delta$, is called the space of harmonic shifted symmetric polynomials. We find an explicit basis for this space using an analogue of the Kelvin transform from the theory of harmonic functions.

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