Stability of the Tangent Bundle of the Wonderful Compactification of an Adjoint Group

Let $G$ be a complex linear algebraic group which is simple of adjoint type. Let $\overline G$ be the wonderful compactification of $G$. We prove that the tangent bundle of $\overline G$ is stable with respect to every polarization on $\overline G$.

2010 Mathematics Subject Classification: 32Q26, 14M27, 14M17

Keywords and Phrases: Wonderful compactification, adjoint group, stability, irreducibility, equivariant bundle

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