Hochschild cohomology of symmetric groups and generating functions

Benson, D., Kessar, R. & Linckelmann, M. (2023). Hochschild cohomology of symmetric groups and generating functions. Journal of Group Theory, doi: 10.1515/jgth-2022-0130

Abstract

In this article, we compute the dimensions of the Hochschild cohomology of symmetric groups over prime fields in low degrees. This involves us in studying some partition identities and generating functions of the dimensions in any fixed degree of the Hochschild cohomology of symmetric groups. We show that the generating function of the dimensions of the Hochschild cohomology in any fixed degree of the symmetric groups differs from that in degree 0 by a rational function.