Commuting Schemes of Upper Triangular Matrices and Representation Homology
Abstract
We establish a connection between generalised commuting schemes Cg(Un) of higher genus g, which are associated with a group scheme Un consisting of upper triangular unipotent matrices, and the representation homology HR*(g,Un) of a Riemann surface g with coefficients in the group Un. As an outcome, we provide a numerical criterion for determining whether commuting schemes C(Un) form a complete intersection.
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