Related papers: Minimal reduction type in classical cases

We check that the statement of Hikita conjecture holds for the case of the minimal nilpotent orbit of a simple Lie algebra $\mathfrak{g}$ of type ADE and $\mathbb{C} ^2 / \Gamma$.

We first show the closure of the minimal nilpotent adjoint orbit Omin^{D_n} in so_{2n} is isomorphic to the affinization of T^*(SL_{n-1}/[P,P]) where P is the parabolic subgroup P_{(1,1,n-3)} of SL_{n-1}(C). Then we prove that the closure…

We establish a novel connection between the minimal nilpotent orbit $\mathbb{O}_n$ in $\mathfrak{sl}_n$ and the minimal nilpotent orbit closure $\overline{\mathbf{O}}_n$ in $\mathfrak{so}_{2n+2}$, which differs from the shared-orbit…

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…

Using the techniques of equivariant bifurcation theory we prove the existence of non-stationary periodic solutions of $\Gamma$-symmetric systems $\ddot q(t)=-\nabla U(q(t))$ in any neighborhood of an isolated orbit of minima $\Gamma(q_0)$…

We introduce the notion of minimal reduction type of an affine Springer fiber, and use it to define a map from the set of conjugacy classes in the Weyl group to the set of nilpotent orbits. We show that this map is the same as the one…

In this paper we study topological cocycles for minimal homeomorphisms on a compact metric space. We introduce a notion of an essential range for topological cocycles with values in a locally compact group, and we show that this notion…

We show that the specialized quantum D-module of the equivariant quantum cohomology ring of the minimal resolution of an ADE singularity is isomorphic to the D-module of graded traces on the minimal nilpotent orbit in the Lie algebra of the…

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…

Let us fix a complex simple Lie algebra and its non-compact real form. This paper focuses on non-zero adjoint nilpotent orbits in the complex simple Lie algebra meeting the real form. We show that the poset consisting of such nilpotent…

We consider the conjugation-action of the Borel subgroup of the symplectic or the orthogonal group on the variety of nilpotent complex elements of nilpotency degree $2$ in its Lie algebra. We translate the setup to a…

In the paper "The Second cohomology of nilpotent orbits in classical Lie algebras, Kyoto J. Math. 60 (2020), no. 2, 717-799" by I. Biswas, P. Chatterjee and C. Maity homotopy types of nilpotent orbits are explicitly described in the case of…

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…

Kirillov's orbit theory provides a powerful tool for the investigation of irreducible unitary representations of many classes of Lie groups. In a previous paper we used a modification hereof, called monomial linearisation, to construct a…

In this paper, we establish a general criterion for good pairs, namely pairs consisting of a nilpotent orbit and an even good grading in a simple Lie algebra, which guarantees the existence of a quantum Hamiltonian reduction between…

We classify completely prime primitive ideals whose associated varieties are the closure of the minimal nilpotent orbit of $\mathfrak{g}=\mathfrak{sl}(n,\mathbb{C})$, and classify irreducible $(\mathfrak{g},\mathfrak{k})$-modules which have…

We show that a doubly minimal system $X$ has the property that for every minimal system $Y$ the orbit closure of any pair $(y,x) \in Y \times X$ is either $Y \times X$ or it has the form $\Gamma_\pi = \{(\pi(x),x) : x \in X\}$ for some…

We consider a system with symmetries whose configuration space is a compact Lie group, acted upon by inner automorphisms. The classical reduced phase space of this system decomposes into connected components of orbit type subsets. To…

We complete the construction of the modular generalized Springer correspondence for an arbitrary connected reductive group, with a uniform proof of the disjointness of induction series that avoids the case-by-case arguments for classical…

In this note we investigate the normality of closures of orthogonal and symplectic nilpotent orbits in positive characteristic. We prove that the closure of such a nilpotent orbit is normal provided that neither type d nor type e minimal…