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We give a short proof of an elementary classical result: any rational symplectic matrix can be put in diagonal form after right and left multiplication by integral symplectic matrices. We also give a short proof for its extension to Chevalley groups due to Steinberg by using the Cartan-Bruhat-Tits decomposition over p-adic fields.

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On the Rational Symplectic Group

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  • 发表日期：

    2025年

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  • Yves Benoist

摘要

We give a short proof of an elementary classical result: any rational symplectic matrix can be put in diagonal form after right and left multiplication by integral symplectic matrices. We also give a short proof for its extension to Chevalley groups due to Steinberg by using the Cartan-Bruhat-Tits decomposition over p-adic fields.