Automorphisms of $\overline{T}$

Abstract

Let $\overline{G}$ be the wonderful compactification of a simple affine algebraic group $G$ defined over $\mathbb{C}$ such that its center is trivial and $G\ne \mathrm{PSL}(2,\mathbb{C})$. Take a maximal torus $T\subset G$, and denote by $\overline{T}$ its closure in $\overline{G}$. We prove that $T$ coincides with the connected component, containing the identity element, of the group of automorphisms of the variety $\overline{T}$.

Final version