Related papers: Orbit closures in the enhanced nilpotent cone

We present a quantization of an isomorphism of Mirkovi\'c and Vybornov which relates the intersection of a Slodowy slice and a nilpotent orbit closure in $\mathfrak{gl}_N$ , to a slice between spherical Schubert varieties in the affine…

In this paper we consider a class of connected closed $G$-manifolds with a non-empty finite fixed point set, each $M$ of which is totally non-homologous to zero in $M_G$ (or $G$-equivariantly formal), where $G={\Bbb Z}_2$. With the help of…

In this note we explicitly construct top-dimensional components of the cyclic convolution varieties. These components correspond (via the geometric Satake equivalence) to irreducible summands $V(\lambda+\mu-N\beta) \subset V(\lambda)…

We study the natural action of $\mathrm{PGL}(V)$ on the Grassmannian $G=\operatorname{Gr}(2,\operatorname{Sym}^2 V^\vee)$, where $\dim V=4$ and points of $G$ are pencils of quadrics in $\mathbb{P}(V)\cong \mathbb{P}^3$. Here $\dim G=16$…

Let $G$ be a connected semi-simple algebraic group of adjoint type over an algebraically closed field, and let $\overline{G}$ be the wonderful compactification of $G$. For a fixed pair $(B, B^-)$ of opposite Borel subgroups of $G$, we look…

The existence of closed orbits of real algebraic groups on real algebraic varieties is established. As an application, it is shown that if G is a real reductive linear group with Iwasawa decomposition G= KAN, then every unipotent subgroup…

E.B. Vinberg developed a theory of homogeneous convex cones $C \subset V= \mathbb{R}^n$, which has many applications. He gave a construction of such cones in terms of non-associative rank $n$ matrix T-algebras $\cal{T}$, that consist of…

Orbits of coadjoint representations of classical compact Lie groups have a lot of applications. They appear in representation theory, geometrical quantization, theory of magnetism, quantum optics etc. As geometric objects the orbits were…

Given a classical semisimple complex algebraic group G and a symmetric pair (G,K) of Hermitian type, we study the closures of the spherical nilpotent K-orbits in the isotropy representation of K. We show that all such orbit closures are…

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 connected reductive algebraic group over $ \C $. We denote by $ K = (G^{\theta})_{0} $ the identity component of the fixed points of an involutive automorphism $ \theta $ of $ G $. The pair $ (G, K) $ is called a symmetric…

We realize certain graded Nakajima varieties of finite Dynkin type as orbit closures of repetitive algebras of Dynkin quivers. As an application, we obtain that the perverse sheaves introduced by Nakajima for describing irreducible…

Let G be a reductive algebraic group over the complex field and O_h be a closed adjoint orbit through a semisimple element h. By a result of Borho and Kraft (1979), it is known that the asymptotic cone of the orbit O_h is the closure of a…

We prove that the orbit closure of the determinant is not normal. A similar result is obtained for the orbit closure of the permanent multiplied by a power of a linear form.

As a generalisation of the periodic orbit structure often seen in reflection or mirror symmetric MHD equilibria, we consider equilibria with other orientation-reversing symmetries. An example of such a symmetry, which is a not a reflection,…

We introduce an alternative combinatorial parametrization of Borel orbits in classical symmetric varieties using matchings of the Corona graph. As an application, we obtain ultra log-concavity and unimodality for the number of Borel orbits…

Let Delta be an Euclidean quiver. We prove that the closures of the maximal orbits in the varieties of representations of Delta are normal and Cohen--Macaulay (even complete intersections). Moreover, we give a generalization of this result…

Let $G$ be a connected Lie group and $\text{Sub}_G$ be the space of closed subgroups of $G$ equipped with the Chabauty topology. In this article, we investigate the existence of invariant random subgroups of $G$ supported on various orbits…

We give a generalization to higher dimensions of Silverman's result on finiteness of integer points in orbits. Assuming Vojta's conjecture, we prove a sufficient condition for morphisms on P^N so that (S,D)-integral points in each orbit are…

The topology of the embedding of the coadjoint orbits of the unitary group U(H) of an in-finite dimensional complex Hilbert space H, as canonically determined subsets of the B-space T_s of symmetric trace class operators, is investigated.…