# Questions tagged [nilpotent-cone]

The nilpotent-cone tag has no usage guidance.

6
questions

4
votes

0
answers

108
views

### When does the null-cone consist entirely of eigenvectors?

Let $V$ be a finite-dimensional representation of a complex reductive Lie algebra $\mathfrak g$.
For our purposes, we may define the null-cone like this: $v\in V$ belongs to the null-cone if and only ...

9
votes

0
answers

496
views

### Naive question about classification of unipotent character sheaves

Let $G$ be a connected reductive algebraic group over (say) $\mathbb{C}$. The set $\hat{G}_u$ of isomorphism classes of unipotent irreducible character sheaves has some complicated classification in ...

10
votes

2
answers

1k
views

### Hall-Littlewood functions and functions on the nilpotent cone

The following observation between the spaces of global sections of line bundles on the nilpotent cone and the Hall-Littlewood polynomials is made in a recent physics preprint 1403.0585. Is this a ...

8
votes

1
answer

218
views

### Cominuscule property of nilpotent orbits

Let $G$ be a complex reductive Lie group, $G/P$ a flag manifold,
and $\Phi: T^* G/P \to {\mathfrak g}^*$ the moment map. So $\Phi(T^* G/P)$ is the closure of a nilpotent orbit.
Lots of classes of ...

7
votes

0
answers

187
views

### Divisibility of all entries in an intersection form

What are situations where one can conclude that all entries of an intersection form are divisible by a fixed integer?
More precisely: $F \subset S$ is a proper connected (usually reducible) half-...

18
votes

2
answers

4k
views

### What does the nilpotent cone represent?

Notation
Let $\mathfrak g$ be a the Lie algebra of an algebraic group $G\subseteq GL(V)$ over a(n algebraically closed) field $k$ (I'm actually thinking $G=GL_n$, so $\mathfrak g=\mathfrak{gl}_n$). ...