Abstract:We classify irreducible unitary representations of the group of all infinite matrices over a $p$-adic field ($p\ne 2$) with integer elements equipped with a natural topology. Any irreducible representation passes through a group $GL$ of infinite matrices over a residue ring modulo $p^k$. Irreducible representations of the latter group are induced from finite-dimensional representations of certain open subgroups.

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中文翻译：

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无穷 𝑝-adic 整数矩阵群的酉表示的描述

摘要：我们用配备自然拓扑的整数元素对 $p$-adic 域 ($p\ne 2$) 上的所有无限矩阵组的不可约幺正表示进行分类。任何不可约表示都通过一组 $GL$ 的无限矩阵在一个残差环模 $p^k$ 上。后一组的不可约表示是从某些开放子群的有限维表示中导出的。

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