Commuting Schemes of Upper Triangular Matrices and Representation Homology

Guanyu Li

doi:10.1016/j.jalgebra.2025.10.006

paper

Commuting Schemes of Upper Triangular Matrices and Representation Homology

arXiv:2403.13953 · doi:10.1016/j.jalgebra.2025.10.006

Abstract

We establish a connection between generalised commuting schemes $C_{g} (U_{n})$ of higher genus $g$ , which are associated with a group scheme $U_{n}$ consisting of upper triangular unipotent matrices, and the representation homology $H R_{*} (I^£_{g}, U_{n})$ of a Riemann surface $I^£_{g}$ with coefficients in the group $U_{n}$ . As an outcome, we provide a numerical criterion for determining whether commuting schemes $C (U_{n})$ form a complete intersection.

Final version, 15 pages