Related papers: On the complement of the Richardson orbit

Let G be an almost simple group over an algebraically closed field k of characteristic zero, let g be its Lie algebra and let B be a Borel subgroup of G. Then B acts with finitely many orbits on the variety N_2 of the nilpotent elements in…

Let $G$ be a simple algebraic group over an algebraically closed field $k$ of characteristic $p$. The classification of the conjugacy classes of unipotent elements of $G(k)$ and nilpotent orbits of $G$ on $\operatorname{Lie}(G)$ is…

The main result of the paper establishes the irreducibility of a large family of nonzero central charge induced modules over Affine Lie algebras for any non standard parabolic subalgebra. It generalizes all previously known partial results…

We consider the conjugation-action of an arbitrary upper-block parabolic subgroup of the general linear group on the variety of nilpotent matrices in its Lie algebra. Lie-theoretically, it is natural to wonder about the number of orbits of…

Motivated by relating the representation theory of the split real and $p$-adic forms of a connected reductive algebraic group $G$, we describe a subset of $2^r$ orbits on the complex flag variety for a certain symmetric subgroup. (Here $r$…

We study a problem concerning parabolic induction in certain $p$-adic unitary groups. More precisely, for $E/F$ a quadratic extension of $p$-adic fields the associated unitary group $G=\mathrm{U}(n,n+1)$ contains a parabolic subgroup $P$…

In this paper we study irreducible modules for loop of $A\rtimes DerA$ with finite dimensional weight spaces. In particular, we show that Larsson's constructed modules of tensor fields exhausted all irreducible modules.

Given partitions $\alpha$, $\beta$, $\gamma$, the short exact sequences $0\to N_\alpha \to N_\beta \to N_\gamma \to 0$ of nilpotent linear operators of Jordan types $\alpha$, $\beta$, $\gamma$, respectively, define a constructible subset…

We introduce and prove numerous new results about the orbits of the $T$-fractal billiard. Specifically, in Section 3, we give a variety of sufficient conditions for the existence of a sequence of compatible periodic orbits. In Section 4, we…

In this paper we give an extension of the Birkhoff--Lewis theorem to some semilinear PDEs. Accordingly we prove existence of infinitely many periodic orbits with large period accumulating at the origin. Such periodic orbits bifurcate from…

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 derive the secular evolution of the orbital elements of a stellar-mass object orbiting a spinning massive black hole. We use the post-Newtonian approximation in harmonic coordinates, with test-body equations of motion for the…

We list all connected components of sets of non-discriminant functions near all {\em parabolic} function singularities (which are the second most important family of singularity classes of smooth functions after {\em simple} singularities).…

We study ad-nilpotent ideals of a parabolic subalgebra of a simple Lie algebra. Any such ideal determines an antichain in a set of positive roots of the simple Lie algebra. We give a necessary and sufficient condition for an antichain to…

We consider the variety of Filippov ($n$-Lie) algebra structures on an $(n+1)$-dimensional vector space. The group $GL_n(K)$ acts on it, and we study the orbit closures with respect to the Zariski topology. This leads to the definition of…

In this paper, we consider the construction of irreducible representations of finite pattern groups in terms of Panov's associative polarization, which is a finite-field analogue of Kirillov's orbital method. Using this construction, first,…

A complex irreducible character of a finite group G is said to be p-constant, for some prime p dividing the order of G, if it takes constant value at the set of p-singular elements of G. In this paper we classify irreducible p-constant…

Given a supercuspidal representation $\sigma$ of a parabolic subgroup $P$ of reductive group $G$, we discover a universal hierarchical structure of reducibility of the parabolic induction $Ind^G_P(\sigma)$, i.e. always irreducible from some…

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 $k$ be a field with a nontrivial discrete valuation which is complete and has perfect residue field. Let $G$ be the group of $k$-rational points of a reductive, linear algebraic group $\textbf{G}$ equipped with an involution $\theta$…