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

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arxiv 2007.15547 v1 pith:M2Q73ZCN submitted 2020-07-30 math.GR math.RAmath.RT

Omer Lavi , Arie Levit This is my paper · ORCID
classification math.GRmath.RAmath.RT
keywords mathrmgroupringcharactersclassifycommutativenoetheriancharacter
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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 $R^d$.

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  1. Stationary characters on lattices of semisimple Lie groups

    math.GR 2019-08 accept novelty 8.0 of 10

    Every stationary character on an irreducible lattice of a higher-rank semisimple Lie group is a genuine character, yielding new rigidity and URS finiteness results.

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