The rapid decay property for pairs of discrete groups

Indira Chatterji; Benjamin Zarka

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arXiv · 2412.07994

The rapid decay property for pairs of discrete groups

Indira Chatterji·Benjamin Zarka

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Abstract

We generalize the notion of rapid decay property for a group $G$ to pairs of groups $(G,H)$ where $H$ is a finitely generated subgroup of $G$, where typically the subgroup $H$ does not have rapid decay. We deduce some isomorphisms in $K$-theory, and investigate relatively spectral injections in the reduced group $C^*$-algebra. Rapid decay property for the pair $(G,H)$ also gives a lower bound for the probability of return to $H$ of symmetric random walks on $G$.

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Indira Chatterji, Benjamin Zarka. 2024-12-11. The rapid decay property for pairs of discrete groups. https://arxiv.org/abs/2412.07994

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