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arXiv · 2309.07282

Centralizer Rigidity near Elements of the Weyl Chamber Flow

Zhijing Wendy Wang
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Abstract

In this paper, we prove centralizer rigidity near an element of the Weyl chamber flow on a semisimple Lie group. We show that a volume preserving perturbation of an element of the Weyl chamber flow on a quotient $G/\Gamma$ of an $\mathbb{R}$-split, simple Lie group $G$ either has centralizer of dimension $0$ or $1$, or is smoothly conjugate to an element of the Weyl chamber flow. We also acquire a general condition for the centralizer of a partially hyperbolic diffeomorphism to be a Lie group.

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Zhijing Wendy Wang. 2023-09-13. Centralizer Rigidity near Elements of the Weyl Chamber Flow. https://arxiv.org/abs/2309.07282

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