I'm studying Chevalley groups and have problems with some basic stuff. Let $G_{\pi}(\Phi,R)$ be a Chevalley group, with $R$ being a local ring, $\Phi$ being an undecomposable root system and $\pi$ being a finitely dimensional faithful representation of seimisimple Lie algebra. How can I calculate the centralizer of single elementary unpotent element $C(x_\alpha(t))$ ( $\alpha \in \Phi$, $t\in R$)? Is it possible to read about it somewhere? I thought it should be a corollary of Chevalley commutator formula: $[x_{\alpha}(t),x_{\beta}(u)] = \prod x_{i\alpha + j\beta}(N_{\alpha\beta ij}t^{i}u^{j})$ but couldn't grasp how exactly it should be used.
2026-03-29 03:02:33.1774753353
Centralizer of elementary unipotent element of Chevalley group over local ring.
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