Related papers: The (cyclic) enhanced nilpotent cone via quiver re…

We give a geometric description for the dominant characteristic of a nilpotent orbit in an arbitrary finite-dimensional rational G-module. In particular, we obtain a generalization of a recent result of Gunnells-Sommers, see…

It is well known that any polycyclic group, and hence any finitely generated nilpotent group, can be embedded into $GL_{n}(\mathbb{Z})$ for an appropriate $n\in \mathbb{N}$; that is, each element in the group has a unique matrix…

Let $G$ be a simply connected algebraic group of type $B,C$ or $D$ over an algebraically closed field of characteristic 2. We construct a Springer correspondence for the dual vector space of the Lie algebra of $G$. In particular, we…

Let $G$ be a simple simply-connected algebraic group over an algebraically closed field $k$ of characteristic $p>0$ with $\mathfrak{g}={\rm Lie}(G)$. We discuss various properties of nilpotent orbits in $\mathfrak{g}$, which have previously…

We show that a finite, connected quiver Q without oriented cycles is a Dynkin or Euclidean quiver if and only if all orbit semigroups of representations of Q are saturated.

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…

Let $G=Sp_{2n}(\mathbb{C})$, and $\mathfrak{N}$ be Kato's exotic nilpotent cone. Following techniques used by Bezrukavnikov in [5] to establish a bijection between $\Lambda^+$, the dominant weights for a simple algebraic group $H$, and…

We give a full classification of 6-dimensional nilpotent Lie algebras over an arbitrary field, including fields that are not algebraically closed and fields of characteristic~2. To achieve the classification we use the action of the…

If $G$ and $H$ are finitely generated residually nilpotent groups, then $G$ and $H$ are in the same nilpotent genus if they have the same lower central quotients (up to isomorphism). A stronger condition is that $H$ is para-$G$ if there…

This article gives a description of the diagonal $GL_3$-orbits on the quadruple projective variety $(\mathbb P^2)^4$. We give explicit representatives of orbits, and describe the closure relations of orbits. A distinguished feature of our…

We propose a systematic and topological study of limits $\lim_{\nu\to 0^+}G_\mathbb{R}\cdot(\nu x)$ of continuous families of adjoint orbits for non-compact simple Lie groups. This limit is always a finite union of nilpotent orbits. We…

Let $\g$ be simple Lie algebra. We give a conceptual proof for the fact that the nilpotent orbits of height 3 are spherical. It is shown that if the highest root of $\g$ is fundamental, then $\g$ has a specific nilpotent orbit of height 3.…

A nilpotent quotient algorithm for finitely presented Lie rings over Z (LieNQ) is described. The paper studies graded and non-graded cases separately. The algorithm computes the so-called nilpotent presentation for a finitely presented,…

Let $O$ be a closed Poisson conjugacy class of the complex algebraic Poisson group GL(n) relative to the Drinfeld-Jimbo factorizable classical r-matrix. Denote by $T$ the maximal torus of diagonal matrices in GL(n). With every $a\in O\cap…

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…

This paper provides a comparison between the $K$-structure of unipotent representations and regular sections of bundles on nilpotent orbits for complex groups of type $D$. Precisely, let $ G_ 0 =Spin(2n,\mathbb C)$ be the Spin complex group…

We extend results on finite dimensional nilpotent Lie algebras to Leibniz algebras and counterexamples to others are found. One generator algebras are used in these examples and are investigated further.

By decomposing the regular representation of a particular (Heisenberg-like) Lie supergroup into irreducible subspaces, we show that not all of them can be obtained by applying geometric quantization to coadjoint orbits with an even…

We define a notion of roundness for finite groups. Roughly speaking, a group is round if one can order its elements in a cycle in such a way that some natural summation operators map this cycle into new cycles containing all the elements of…

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.