Characters of the group ${\mathrm{EL}}_d(R)$ for a commutative Noetherian ring $R$

Abstract

Let $R$ be a commutative Noetherian ring with unit. We classify the characters of the group ${\mathrm{EL}}_d(R)$ provided that $d$ is greater than the stable range of the ring $R$. It follows that every character of ${\mathrm{EL}}_d(R)$ is induced from a finite dimensional representation. Towards our main result we classify ${\mathrm{EL}}_d(R)$-invariant probability measures on the Pontryagin dual group of $R^d$.

51 pages