We classify the irreducible representations of smooth, connected affine algebraic groups over a field, by tackling the case of pseudo-reductive groups. We reduce the problem of calculating the dimension for pseudo-split pseudo-reductive groups to the split reductive case and the pseudo-split pseudo-reductive commutative case. Moreover, we give the first results on the latter, including a rather complete description of the rank one case.

中文翻译：

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伪约简群的不可约模

我们通过处理伪约简群的情况，对域上光滑、连通的仿射代数群的不可约表示进行分类。我们将计算伪分裂伪约简群的维数问题简化为分裂约简情况和伪分裂伪约约交换情况。此外，我们给出了后者的第一个结果，包括对等级一案例的相当完整的描述。