Related papers: On the centralizer of a balanced nilpotent section

Let $G$ be a semisimple algebraic group over the complex numbers and $K$ be a connected reductive group mapping to $G$ so that the Lie algebra of $K$ gets identified with a symmetric subalgebra of $\mathfrak{g}$. So we can talk about…

We introduce a new construction, the isotropy groupoid, to organize the orbit data for split $\Gamma$-spaces. We show that equivariant principal $G$-bundles over split $\Gamma$-CW complexes $X$ can be effectively classified by means of…

Let G be an algebraic group and let X be a generically free G-variety. We show that X can be transformed, by a sequence of blowups with smooth G-equivariant centers, into a G-variety X' with the following property: the stabilizer of every…

If $G$ is a finite group, the Grothendieck group ${\mathbf{K}}\_G(G)$ of the category of $G$-equivariant ${\mathbb{C}}$-vector bundles on $G$ (for the action of $G$ on itself by conjugation) is endowed with a structure of (commutative)…

Let $\mathbf G$ be a connected reductive algebraic group over an algebraically closed field, and let $s\in\mathbf G$ be a semisimple element. We show that the centraliser of $s$ is the semi-direct product of its identity component by its…

Let $G$ be a finite group and $\sigma=\{\sigma_{i}|i\in I\}$ be a partition of the set of all primes $\mathbb{P}$, that is, $\mathbb{P}=\bigcup_{i\in I}\sigma_{i}$ and $\sigma_{i}\cap \sigma_{j}=\emptyset$ for all $i\neq j$. A chief factor…

An action of a complex reductive group $\mathrm G$ on a smooth projective variety $X$ is regular when all regular unipotent elements in $\mathrm G$ act with finitely many fixed points. Then the complex $\mathrm G$-equivariant cohomology…

Let G be a connected reductive linear algebraic group defined over an algebraically closed field of characteristic p. Assume that p is good for G. In this note we classify all the spherical nilpotent G-orbits in the Lie algebra of G. The…

In the Hilbert scheme of points on a scheme X there is an open subset parameterizing distinct points. The closure of that open set is by definition the good component. When X is flat over the base, we show that a certain blow-up of the…

The non-solvable graph of a finite group G is a simple graph whose vertices are the elements of G and there is an edge between x and y if and only if the subgroup generated by x and y is not solvable. The isolated vertices in the…

Consider a nonsolvable finite group G, where R(G) represents the solvable radical of G. For any element x in G, the solvabilizer of x in G, denoted by Sol_G(x), is defined as the set of all elements y in G such that the subgroup generated…

The universal centralizer of a semisimple algebraic group is the family of centralizers of regular elements, parametrized by their conjugacy classes. When the group is of adjoint type, we construct a smooth, log-symplectic fiberwise…

For any group G, let C(G) denote the intersection of the normal- izers of centralizers of all elements of G. Set C0 = 1. Define Ci+1(G)=Ci(G) = C(G=Ci(G)) for i ? 0. By C1(G) denote the terminal term of the ascending series. In this paper,…

Let $G$ be a connected reductive group acting on a complex vector space $V$ and projective space ${\mathbb P}V$. Let $x\in V$ and ${\cal H}\subseteq {\cal G}$ be the Lie algebra of its stabilizer. Our objective is to understand points…

Let $R$ be a discrete valuation ring with fraction field $K$ and $X$ a flat $R$-scheme. Given a faithful action of a $K$-group scheme $G_K$ over the generic fibre $X_K$, we study models $G$ of $G_K$ acting on $X$. In various situations, we…

Let $G$ be an adjoint algebraic group of type $B$, $C$, or $D$ over an algebraically closed field of characteristic 2. We construct a Springer correspondence for the Lie algebra of $G$. In particular, for orthogonal Lie algebras in…

Let $G$ be the complex exceptional Lie group of type $G_2$. Among the five nilpotent orbits in its Lie algebra $\mathfrak{g}$, only the 8-dimensional orbit $\mathcal{O}_8$ has non-normal orbit closure $\bar{\mathcal{O}_8}$. In this short…

We complete the proof of the Nisnevich conjecture in equal characteristic: for a smooth algebraic variety $X$ over a field $k$, a $k$-smooth divisor $D \subset X$, and a reductive $X$-group $G$ whose base change $G_D$ is totally isotropic,…

Let G be a real, connected, noncompact, semisimple Lie group, let K be a maximal compact subgroup of G, and let g=k+p be the corresponding Cartan decomposition of the complexified Lie algebra of G. Sequences of strongly orthogonal…

The solubility graph $\Gamma_S(G)$ associated with a finite group $G$ is a simple graph whose vertices are the elements of $G$, and there is an edge between two distinct vertices if and only if they generate a soluble subgroup. In this…