Related papers: Pieces of nilpotent cones for classical groups

We define a set of "enhanced" nilpotent quiver representations that generalizes the enhanced nilpotent cone. This set admits an action by an associated algebraic group $K$ with finitely many orbits. We define a combinatorial set that…

In this article, we investigate an analogue of the global nilpotent cone in the case of the cotangent stack of the moduli stack of parahoric torsors on curves.

Coulomb branches of a set of $3d\ \mathcal{N}=4$ supersymmetric gauge theories are closures of nilpotent orbits of the algebra $\mathfrak{so}(n)$. From the point of view of string theory, these quantum field theories can be understood as…

The $\mathrm{GL}(V)$-orbits in the enhanced nilpotent cone $V\times\mathcal{N}(V)$ are (essentially) in bijection with the orbits of a certain parabolic $P\subseteq\mathrm{GL}(V)$ (the mirabolic subgroup) in the nilpotent cone…

In this paper we consider the problem of classification of nilpotent orbits for the pseudo-quaternionic coset manifolds U/H* obtained in the time-like dimensional reduction of N = 2 supergravity models based on homogeneous symmetric special…

The purpose of this note is to present a short elementary proof of a theorem due to Faltings and Laumon, saying that the global nilpotent cone is a Lagrangian substack in the cotangent bundle of the moduli space of G-bundles on a complex…

We continue the study of the closures of $GL(V)$-orbits in the enhanced nilpotent cone $V\times\cN$ begun by the first two authors. We prove that each closure is an invariant-theoretic quotient of a suitably-defined enhanced quiver variety.…

In this manuscript, we compute explicitly the Lusztig-Vogan bijection for local systems of some classical, special, nilpotent orbits. Using these results, we prove a conjecture of Achar and Sommers on regular functions of some covers of…

We prove that a nilpotent subgroup of orientation preserving $C^{1}$ diffeomorphisms of ${\mathbb S}^{2}$ has a finite orbit of cardinality at most two. We also prove that a finitely generated nilpotent subgroup of orientation preserving…

In this paper we prove a new characterization of the distinguished unipotent orbits of a connected reductive group over an algebraically closed field of characteristic 0. For classical groups we prove the characterization by a combinatorial…

We determine the non-reduced components of global nilpotent cones in various cases of interest. In particular, under the appropriate coprimality conditions, we show: (1) the global nilpotent cone for an $L$-twisted…

An $n\times n$ nilpotent matrix $B$ is determined up to conjugacy by a partition $P_B$ of $n$, its Jordan type given by the sizes of its Jordan blocks. The Jordan type $\mathfrak D(P)$ of a nilpotent matrix in the dense orbit of the…

We study the ring of regular functions of classical spherical orbits $R(\mathcal{O})$ for $G = Sp(2n,\mathbb{C})$. In particular, treating $G$ as a real Lie group with maximal compact subgroup $K$, we focus on a quantization model of…

We prove that a locally nilpotent group $G$ of $C^{1}$ diffeomorphisms of a compact surface $S$ of non-vanishing Euler characteristic has a finite orbit ${\mathcal O}$ whose cardinal is bounded by above by a function of the characteristic…

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…

Let $\mathfrak b_n(\mathbb F_q)$ denote the Lie algebra of upper triangular $n\times n$ matrices over the finite field $\mathbb F_q$, and let $\mathfrak u_n(\mathbb F_q)$ be the nilradical of $\mathfrak b_n$. For every $\mathfrak…

We prove the Box Conjecture for pairs of commuting nilpotent matrices, as formulated by Iarrobino et al [28]. This describes the Jordan type of the dense orbit in the nilpotent commutator of a given nilpotent matrix. Our main tool is the…

We define and study an exotic t-structure on the bounded derived category of equivariant coherent sheaves on partial resolutions of the nilpotent cone.

Let $N$ be a point of an orbit closure $\bar{O_M}$ in a module variety such that its orbit $O_N$ has codimension two in $\bar{O_M}$. We show that under some additional conditions the pointed variety $(\bar{O_M},N)$ is smoothly equivalent to…

With the help of Lusztig's canonical basis, we study local intersection cohomology of the Zariski closures of orbits of representations of a quiver of type A, D or E. In particular, we characterize the rationally smooth orbits and prove…