Related papers: On Quantization of a Nilpotent Orbit Closure in $G…

We consider aspects of the geometry and topology of nilpotent orbits in finite-dimensional complex simple Lie algebras. In particular, we give the equivariant cohomologies of the regular and minimal nilpotent orbits with respect to the…

The stationary solutions of a large variety of (super)gravity theories can be described within a non-linear sigma model G / H* coupled to Euclidean gravity in three-dimensions, for which G is a simple group and H* a non-compact real form of…

Suppose that $G$ is a finite solvable group and $V$ is a finite, faithful and completely reducible $G$-module. Let $N$ be a nilpotent subgroup of $G$, then there exits $v \in V$ such that $|\bC_N(v)| \leq (|N|/p)^{1/p}$, where $p$ is the…

We first show the closure of the minimal nilpotent adjoint orbit Omin^{D_n} in so_{2n} is isomorphic to the affinization of T^*(SL_{n-1}/[P,P]) where P is the parabolic subgroup P_{(1,1,n-3)} of SL_{n-1}(C). Then we prove that the closure…

Let $\sigma$ be an involution of a complex semisimple Lie algebra $\mathfrak g$ and $\mathfrak g=\mathfrak g_0\oplus\mathfrak g_1$ the related $\mathbb Z_2$-grading. We study relations between nilpotent $G_0$-orbits in $\mathfrak g_0$ and…

We study the local properties of a class of codimension-2 defects of the 6d N=(2,0) theories of type J=A,D,E labeled by nilpotent orbits of a Lie algebra \mathfrak{g}, where \mathfrak{g} is determined by J and the outer-automorphism twist…

We study deformations of orbit closures for the action of a connected semisimple group $G$ on its Lie algebra $\mathfrak{g}$, especially when $G$ is the special linear group. The tools we use are on the one hand the invariant Hilbert scheme…

Let i be a homomorphism of the multiplicative group into a connected reductive algebraic group over C. Let G^i be the centralizer of the image i. Let LG be the Lie algebra of G and let L_nG (n integer) be the summands in the direct sum…

This paper completes the classification of seven-dimensional nilpotent Lie groups endowed with a left-invariant purely coclosed $\text{G}_2$-structure, initiated by the first-named author and collaborators. In this previous work, the…

Let g be a real form of a simple complex Lie algebra. Based on ideas of Djokovic and Vinberg, we describe an algorithm to compute representatives of the nilpotent orbits of g using the Kostant-Sekiguchi correspondence. Our algorithms are…

We investigate the existence of left-invariant closed G$_2$-structures on seven-dimensional non-solvable Lie groups, providing the first examples of this type. When the Lie algebra has trivial Levi decomposition, we show that such a…

This paper is about nilpotent orbits of reductive groups over local non-Archimedean fields. In this paper we will try to identify for which groups there are only finitely many nilpotent orbits, for which groups the nilpotent orbits are…

We construct quantization of semisimple conjugacy classes of the exceptional group $G=G_2$ along with and by means of their exact representations in highest weight modules of the quantum group $U_q(\mathfrak{g})$. With every point $t$ of a…

We study closures of conjugacy classes in the symmetric matrices of the orthogonal group and we determine which one are normal varieties. In contrast to the result for the symplectic group where all classes have normal closure, there is…

Let $G=\mathrm{GL}_n(\mathbb{F})$, $\mathrm{O}_n(\mathbb{F})$, or $\mathrm{Sp}_{2n}(\mathbb{F})$ be one of the classical groups over an algebraically closed field $\mathbb{F}$ of characteristic $0$, let $\breve{G}$ be the MVW-extension of…

The existence of closed orbits of real algebraic groups on certain real algebraic spaces is established. As an application it is shown that if $G$ is a real reductive group with Iwasawa decomposition $G=KAN$, then all unipotent subgroups of…

Let $G$ be a split reductive algebraic group defined over a complete discrete valuation ring $\mathbb{O}$, with residue field $\mathbb{F}$ and fraction field $\mathbb{K}$, where the fiber $G_{\mathbb{F}}$ is geometrically standard. A…

We show that there is a consistent polynomial quantization of the coordinate ring of a basic nilpotent coadjoint orbit of a semisimple Lie group. We also show, at least in the case of a nilpotent orbit in sl(2,R)*, that any such…

Let $G$ be a connected linear algebraic group, let $V$ be a finite dimensional algebraic $G$-module, and let $\mathcal O_1$, $\mathcal O_2$ be two $G$-orbits in $V$. We describe a constructive way to find out whether $\mathcal O_1$ lies in…

Recently, V.Ginzburg introduced and studied in depth the notion of a principal nilpotent pair in a semisimple Lie algebra \g. Our aim is to contribute to the general theory of nilpotent pairs. Roughly speaking, a nilpotent pair (e_1,e_2)…