On some 𝑝-adic and mod 𝑝 representations of quaternion algebra over ℚ𝑝

Yongquan Hu, Haoran Wang
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Abstract

Let 𝐷 be the nonsplit quaternion algebra over Q p \mathbb{Q}_{p} . We prove that a class of admissible unitary Banach space representations of D × D^{\times} of global origin are topologically of finite length.
关于ℚ𝑝上四元代数的一些𝑝和模𝑝表示
让 𝐷 是 Q p 上的非分裂四元数代数。我们证明,全局原点的 D × D^{\times} 的一类可容许的单元巴纳赫空间表示在拓扑上是有限长的。
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