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YCor
YCor
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Stabilizers for Nilpotent Adjoint Orbitsnilpotent adjoint orbits of Semisimple Groupssemisimple groups

Let $G$ be a connected, simply-connected, complex, semisimple Lie group with Lie algebra $\frak{g}$. Suppose that $X\in\frak{g}$ is a nilpotent element (iei.e. that $ad_X:\frak{g}\rightarrow\frak{g}$ is a nilpotent endomorphism), and let $C_G(X)\subseteq G$ denote its stabilizer with respect to the adjoint representation of $G$. What is known about the topology of $C_G(X)$ (ex. topological invariants)? I would appreciate any and all references/suggestions, particularly those concerning the stabilizers of irregular nilpotent elements of $\frak{g}$.

Thanks!

Stabilizers for Nilpotent Adjoint Orbits of Semisimple Groups

Let $G$ be a connected, simply-connected, complex, semisimple Lie group with Lie algebra $\frak{g}$. Suppose that $X\in\frak{g}$ is a nilpotent element (ie. that $ad_X:\frak{g}\rightarrow\frak{g}$ is a nilpotent endomorphism), and let $C_G(X)\subseteq G$ denote its stabilizer with respect to the adjoint representation of $G$. What is known about the topology of $C_G(X)$ (ex. topological invariants)? I would appreciate any and all references/suggestions, particularly those concerning the stabilizers of irregular nilpotent elements of $\frak{g}$.

Thanks!

Stabilizers for nilpotent adjoint orbits of semisimple groups

Let $G$ be a connected, simply-connected, complex, semisimple Lie group with Lie algebra $\frak{g}$. Suppose that $X\in\frak{g}$ is a nilpotent element (i.e. that $ad_X:\frak{g}\rightarrow\frak{g}$ is a nilpotent endomorphism), and let $C_G(X)\subseteq G$ denote its stabilizer with respect to the adjoint representation of $G$. What is known about the topology of $C_G(X)$ (ex. topological invariants)? I would appreciate any and all references/suggestions, particularly those concerning the stabilizers of irregular nilpotent elements of $\frak{g}$.

Thanks!

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Peter Crooks
Peter Crooks
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Stabilizers for Nilpotent Adjoint Orbits of Semisimple Groups

Let $G$ be a connected, simply-connected, complex, semisimple Lie group with Lie algebra $\frak{g}$. Suppose that $X\in\frak{g}$ is a nilpotent element (ie. that $ad_X:\frak{g}\rightarrow\frak{g}$ is a nilpotent endomorphism), and let $C_G(X)\subseteq G$ denote its stabilizer with respect to the adjoint representation of $G$. What is known about the topology of $C_G(X)$ (ex. topological invariants)? I would appreciate any and all references/suggestions, particularly those concerning the stabilizers of irregular nilpotent elements of $\frak{g}$.

Thanks!