# Questions tagged [nilpotent-orbits]

These are the adjoint orbits of a complex semisimple group lying in the nilpotent cone. Nilpotent orbits arise in algebraic geometry, symplectic geometry, and representation theory.

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### Vanishing of power of nilpotent operator $\mathrm{ad} \, \;e$ in different characteritics

This question needs some background: (1) In his influential 1959 paper here, Kostant studied the adjoint representation of a simple Lie algebra $\mathfrak{g}$ over $\mathbb{C}$ (which can be ...
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### Affine analog of the theory of sheets

In the study of adjoint orbits in a complex semi-simple lie algebra, there is a well known object known as a "sheet". These are the irreducible components of the union of orbits of the same dimension. ...
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### Differential of the adjoint quotient map

My question is regarding a paper by R.W Richardson titled "Derivatives of invariant polynomials on a semisimple Lie Algebra" ** . In this paper, he reports on computations of the rank of the ...
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### Equality of codimension under Lusztig-Spaltenstein induction

Pardon if this is well known. Suppose I have a (say complex) connected reductive group $G^{\vee}$ with the $\tilde{\Delta}=\Delta\cup\{\alpha_0\}$ being the simple roots plus the negative highest root ...
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### Wavefront sets of irreducible representations with non-integral infinitesimal characters

Let $G$ be a complex reductive algebraic group (connected, simply connected etc), viewed as a real group. We study the representations of $G$, and we follow the notations in the paper of Barbasch and ...
Let $G$ be a simple algebraic group over the algebraically closed field $k$ of positive characteristic, and let ${\mathfrak g}={\rm Lie}(G)$. It is well known that there are finitely many nilpotent $G$...