Related papers: Nilpotent cones and adjoint orbits

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.

We show that a locally symmetric space of noncompact type and with finite volume is quasi-isometric to the euclidean cone over a finite simplicial complex. A detailed analysis of metric properties yields a proof of a conjecture of Siegel.

We consider faithful actions of simple algebraic groups on self-dual irreducible modules, and on the associated varieties of totally singular subspaces, under the assumption that the dimension of the group is at least as large as the…

We provide sufficient conditions for a free amalgamated product of torsionfree nilpotent groups to be residually nilpotent. We also characterise the residual nilpotence of certain higher-dimensional amalgams of unipotent groups over the…

In this article some noncommutative topological objects such as NC mapping cone and NC mapping cylinder are introduced. We will see that these objects are equipped with the NCCW complex structure of [PEDERSEN]. As a generalization we…

I announce a solution of the conjecture about the measure of periodic points for planar billiard tables. The theorem says that if $\Om\subset\R^2$ is a compact domain with piecewise $C^3$ boundary, then the set of periodic orbits for the…

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…

We show existence of relative periodic orbits (a.k.a. relative nonlinear normal modes) near relative equilibria of a symmetric Hamiltonian system under an appropriate assumption on the Hessian of the Hamiltonian. This gives a relative…

We provide an explicit construction for a complete set of orthogonal primitive idempotents of finite group algebras over nilpotent groups. Furthermore, we give a complete set of matrix units in each simple epimorphic image of a finite group…

This paper deals with singularities of closures of $2$-nilpotent Borel conjugacy classes in either a $\text{GL}_n$-conjugacy class or in the nilpotent cone of $\text{GL}_n$. In the latter case we construct a resolution of singularities, in…

For a complex semi-simple Lie algebra, every nilpotent orbit in its projectivization comes with a complex contact structure. For each nilpotent orbit, we classify projective Legendrian subvarieties that are homogeneous under the actions of…

Let D(e) denote the weighted Dynkin diagram of a nilpotent element $e$ in complex simple Lie algebra $\g$. We say that D(e) is divisible if D(e)/2 is again a weighted Dynkin diagram. (That is, a necessary condition for divisibility is that…

A closed subgroup $H$ of a connected reductive group $G$ is called $\textit{spherical}$ if a Borel subgroup in $G$ has an open orbit on $G/H$. We give a combinatorial characterization for a spherical subgroup to be contained in another one…

Let $\mathfrak{g}$ be a simple classical Lie algebra over $\mathbb{C}$ and $G$ be the adjoint group. Consider a nilpotent element $e\in \mathfrak{g}$, and the adjoint orbit $\mathbb{O}=Ge$. The formal slices to the codimension $2$ orbits in…

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…

We present a one-to-one correspondence between equivalence classes of unitary irreducible representations and coadjoint orbits for a class of pro-Lie groups including all connected locally compact nilpotent groups and arbitrary infinite…

This paper is concerned with the study of the rolling without slipping of a dynamically symmetric (in particular, homogeneous) heavy ball on a cone which rotates uniformly about its symmetry axis. The equations of motion of the system are…

Let G be a quasisimple algebraic group over an algebraically closed field of characteristic p>0. We suppose that p is very good for G; since p is good, there is a bijection between the nilpotent orbits in the Lie algebra and the unipotent…

In this article we study the homology of nilpotent groups. In particular a certain vanishing result for the homology and cohomology of nilpotent groups is proved.

A nilpotent orbit $O$ of a complex semisimple Lie algebra $\mathfrak{g}$ has finite fundamental group. Associated with an etale cover of $O$, we have a finite cover of the closure $\bar{O}$ of $O$. In this article we consider the finite…