Related papers: Sheets, slice induction and G2(2) case

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…

The present work is a part of a larger program to construct explicit combinatorial models for the (indecomposable) regular representation of the nilpotent factor $N$ in the Iwasawa decomposition of a semi-simple Lie algebra $\mathfrak g$,…

We introduce the partial reductions and inverse Hamiltonian reductions between affine $\mathcal{W}$-algebras along the closure relations of associated nilpotent orbits in the case of $\mathfrak{sl}_4$, fulfilling all the missing…

Lie bialgebras occur as the principal objects in the infinitesimalisation of the theory of quantum groups - the semi-classical theory. Their relationship with the quantum theory has made available some new tools that we can apply to…

In this paper we shall study symplectic resolutions of a nilpotent orbit closure of a complex simple Lie algebra \g. We shall introduce an equivalence relation in the set of parabolic subgroups of $G$ in terms of marked Dynkin diagrams. We…

The concept of breadth has been used in the classification of p-groups and nilpotent Lie algebras. In this paper, we investigate this notion for finite-dimensional solvable Lie algebras. Our main focus is to characterize solvable Lie…

Motivated by geometric Langlands, we initiate a program to study the mirror symmetry between nilpotent orbit closures of a semisimple Lie algebra and those of its Langlands dual. The most interesting case is $B_n$ via $C_n$. Classically,…

This short note is a supplement to the previous article with the same title. Here we treat a conical symplectic variety obtained as a finite covering of a (not necessarily normal) nilpotent orbit closure of a complex semisimple Lie algebra.

Let $G$ be an adjoint algebraic group of type $B$, $C$, or $D$ over an algebraically closed field of characteristic 2. We construct a Springer correspondence for the Lie algebra of $G$. In particular, for orthogonal Lie algebras in…

In this paper, we study gravitational symmetry algebras that live on 2-dimensional cuts $S$ of asymptotic infinity. We define a notion of wedge algebra $\mathcal{W}(S)$ which depends on the topology of $S$. For the cylinder $S=\mathbb{C}^*$…

We show that the finite dimensional nilpotent complex Lie superalgebras g whose injective hulls of simple U(g)-modules are locally Artinian are precisely those whose even part g_0 is isomorphic to a nilpotent Lie algebra with an abelian…

In this article, we discuss the category $\mathcal{SN}_2$ where the objects are finite-dimensional nilpotent Lie superalgebras of class two and the category $\mathcal{SSKE}$ where the objects are skew-supersymmetric bilinear maps. We…

We study the existence of invariant metrics with holonomy $G_{2(2)}^* \subset SO(4,3)$ on compact nilmanifolds, i.e. on compact quotients of nilpotent Lie groups by discrete subgroups. We prove that, up to isomorphism, there exists only one…

Let $X$ be a smooth projective variety over the complex numbers and $S(d)$ the scheme parametrizing $d$-dimensional Lie subalgebras of $H^0(X,\mathcal{T} X)$. This article is dedicated to the study of the geometry of the moduli space…

Using D2-brane probes, we study various properties of M-theory on singular, non-compact manifolds of G_2 and Spin(7) holonomy. We derive mirror pairs of N=1 supersymmetric three-dimensional gauge theories, and apply this technique to…

We provide an explicit combinatorial description of highest weights of simple highest weight modules over the simple affine vertex algebra of type A of admissible level k. For admissible simple highest weight modules corresponding to the…

This is a short presentation of some classical results on finite dimensional complex Lie algebras (classification of nilpotent Lie algebras, deformations and perturbations, contractions and rigidity). We present some applications to…

We study the existence of certain characteristically nilpotent Lie algebras with flat coadjoint orbits. Their connected, simply connected Lie groups admit square-integrable representations modulo the center. There are many examples of…

The decomposition problem of the enveloping algebra of a simple Lie algebra is reconsidered combining both the analytical and the algebraic approach, showing its relation with the internal labelling problem with respect to a nilpotent…

The analysis and the classification of all reductions for the nonlinear evolution equations solvable by the inverse scattering method is an interesting and still open problem. We show how the second order reductions of the N-wave…