Related papers: The orbit structure of Dynkin curves

Let $G$ be a classical linear algebraic group over an algebraically closed field, and let $\mathfrak{n}$ denote the subset of nilpotent elements in its Lie algebra. In this paper we study a partial order on the $G$-orbits in $\mathfrak{n}$…

Let $\mathfrak{m}$ be a nilpotent ideal in the Borel subalgebra $\mathfrak{b}$ of a complex finite-dimensional semisimple Lie algebra, and $\mathfrak{m}^{\bullet}$ the subset of (ad-)nilpotent elements in $\mathfrak{b}$ such that…

Let X be an F-rational nilpotent element in the Lie algebra of a connected and reductive group G defined over the ground field F. Suppose that the Lie algebra has a non-degenerate invariant bilinear form. We show that the unipotent radical…

Let $G$ be a reductive algebraic group and let $Z$ be the stabilizer of a nilpotent element $e$ of the Lie algebra of $G$. We consider the action of $Z$ on the flag variety of $G$, and we focus on the case where this action has a finite…

The orbital varieties are the irreducible components of the intersection between a nilpotent orbit and a Borel subalgebra of the Lie algebra of a reductive group. There is a geometric correspondence between orbital varieties and irreducible…

In this paper, we give a characterization of the action of any abelian subgroup G of GL(n, C) on C^n. We prove that any orbit of G is regular with order m<=2n. Moreover, we give a method to determine this order. In the other hand, we…

Let $SP_n(\mathbb{C})$ be the symplectic group and $\mathfrak{sp}_n(\mathbb{C})$ its Lie algebra. Let $B$ be a Borel subgroup of $SP_n(\mathbb{C} )$, $\mathfrak{b}={\rm Lie}(B)$ and $\mathfrak n$ its nilradical. Let $\mathcal X$ be a…

Let $G$ be a simple algebraic group and $\mathcal O$ a nilpotent orbit in $\mathfrak g$. Let ${\mathbf{CS}}(\mathcal O)$ denote the affine cone over the secant variety of $\overline{\mathbb P\mathcal O}\subset \mathbb P\mathfrak g$. Using…

We construct by geometric methods a noncommutative model E of the algebra of regular functions on the universal (2-fold) cover M of certain nilpotent coadjoint orbits O for a complex simple Lie algebra g. Here O is the dense orbit in the…

Let $G$ be a connected reductive algebraic group defined over an algebraically closed field $\mathbbm k$ of characteristic zero. We consider the commuting variety $\mathcal C(\mathfrak u)$ of the nilradical $\mathfrak u$ of the Lie algebra…

In this paper, we give a characterization for any abelian subgroup G of a lie group of diffeomorphisms maps of C^n, having a somewhere dense orbit G(x), x in C^n: G(x) is somewhere dense in C^n if and only if there are f_{1},....,f_{2n+1 in…

Suppose that a finite solvable group $G$ acts faithfully, irreducibly and quasi-primitively on a finite vector space $V$. Then $G$ has a uniquely determined normal subgroup $E$ which is a direct product of extraspecial $p$-groups for…

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…

Let N \subseteq M be von Neumann algebras and E:M\to N a faithful normal conditional expectation. In this work it is shown that the similarity orbit S(E) of E by the natural action of the invertible group of G_M of M has a natural complex…

Let $\bar{G}$ be the simple algebraic supergroup $\mathrm{SL}(m|n)$ or $\mathrm{OSp}(m|2n)$ over $\mathbb{C}$. Let $\mathfrak{g}=\mathrm{Lie}(\bar{G})=\mathfrak{g}_{\bar{0}}\oplus\mathfrak{g}_{\bar{1}}$ and let $G=\bar{G}(\mathbb{C})$ where…

Let $G$ be a simple algebraic group and $\ggg=\Lie(G)$ over $k=\bar\bbf_q$ where $q$ is a power of the prime characteristic of $k$, and $F$ a Frobenius morphism on $G$ which can be defined naturally on $\ggg$. In this paper, we investigate…

We organize the nilpotent orbits in the exceptional complex Lie algebras into series using the triality model and show that within each series the dimension of the orbit is a linear function of the natural parameter a=1,2,4,8, respectively…

Let $\FRAK{g}$ be a classical simple Lie superalgebra. To every nilpotent orbit $\cal O$ in $\FRAK{g}_0$ we associate a Clifford algebra over the field of rational functions on $\cal O$. We find the rank, $k(\cal O)$ of the bilinear form…

Let G be a connected reductive complex algebraic group and B a Borel subgroup of G. We consider a subgroup H of B acting with finitely many orbits on the flag variety G/B, and we classify the H-orbits in G/B in terms of suitable…

Let $G$ be a simply connected semisimple algebraic group with Lie algebra $\mathfrak g$, let $G_0 \subset G$ be the symmetric subgroup defined by an algebraic involution $\sigma$ and let $\mathfrak g_1 \subset \mathfrak g$ be the isotropy…