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arXiv · 2111.04232

The cohomology of $p$-adic distribution representations

Weibo Fu
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Abstract

We give a generalization of Kostant's theorem on Lie algebra cohomology of finite dimensional highest weight representations to some infinite dimensional cases over a $p$-adic family of highest weight distribution representations. For proving this, we develop a theory of eigen orthonormalizable Banach representations of $p$-adic torus over an affinoid algebra, and we construct an eigen orthonormalizable weight completion of the distribution representations.

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Weibo Fu. 2021-11-08. The cohomology of $p$-adic distribution representations. https://arxiv.org/abs/2111.04232

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