Related papers: A quantum Mirkovi\'c-Vybornov isomorphism

The Slodowy slice is a flat Poisson deformation of its nilpotent part, and it was demonstrated by Lehn-Namikawa-Sorger that there is an interesting infinite family of nilpotent orbits in symplectic Lie algebras for which the slice is not…

We apply results from the geometry of nilpotent orbits and nilpotent Slodowy slices, together with modularity and asymptotic analysis of characters, to prove many new isomorphisms between affine W-algebras and affine Kac-Moody vertex…

We give a geometric proof of inverse Hamiltonian reduction for all finite W-algebras in type $A$, a certain embedding of the finite W-algebra corresponding to an arbitrary nilpotent in $\mathfrak{gl}_N$ into that corresponding to a larger…

We give a geometric proof of inverse Hamiltonian reduction for all affine W-algebras in type A at generic level, a certain embedding of the affine W-algebra corresponding to an arbitrary nilpotent in $\mathfrak{gl}_N$ into that…

Let g be a semisimple Lie algebra over an algebraically closed field K of characteristic 0 and O be a nilpotent orbit in g. Then Orb is a symplectic algebraic variety and one can ask whether it is possible to quantize $\Orb$ (in an…

We investigate the irreducibility of the nilpotent Slodowy slices that appear as the associated variety of W-algebras. Furthermore, we provide new examples of vertex algebras whose associated variety has finitely many symplectic leaves.

Let g be a complex simple Lie algebra and e a nilpotent element in g. To a certain nilpotent subalgebra m attached to e, called an admissible subalgebra of g, we associate an endomorphism algebra H. When m is constructed from a good grading…

We study general properties of quantisations of Slodowy slices and discuss in detail the case of the minimal nilpotent orbit. Associated varieties of related primitive ideals of U(g) are determined, in the general case, and the de Vos-van…

Let $G$ be a simply connected semisimple algebraic group with Lie algebra $\mathfrak g$, let $G_0 \subset G$ be the symmetric subgroup defined by an algebraic involution $\sigma$ and let $\mathfrak g_1 \subset \mathfrak g$ be the isotropy…

Every conic symplectic singularity admits a universal Poisson deformation and a universal filtered quantization, thanks to the work of Losev and Namikawa. We begin this paper by showing that every such variety admits a universal equivariant…

This is a copy of the article published in IMRN (2007). I describe the noncommutative Batalin-Vilkovisky geometry associated naturally with arbitrary modular operad. The classical limit of this geometry is the noncommutative symplectic…

We introduce parabolic presentations of twisted Yangians of types AI and AII, interpolating between the R-matrix presentation and the Drinfeld presentation. Then we formulate and provide parabolic presentations for the shifted twisted…

We derive explicit formulas for lambda-brackets of the affine classical W-algebras attached to the minimal and short nilpotent elements of any simple Lie algebra g. This is used to compute explicitly the first non-trivial PDE of the…

In this paper we prove the existence of isomorphisms between certain non-commutative algebras that are interesting from representation theoretic perspective and arise as quantizations of certain Poisson algebras. We show that quantizations…

We study a class of varieties which generalize the classical orbital varieties of Joseph. We show that our generalized orbital varieties are the irreducible components of a Mirkovic-Vybornov slice to a nilpotent orbit, and can be labeled by…

Given a pair of nilpotent orbits in a simple Lie algebra, one can associate a pair of vertex algebras called affine W-algebras. Under some compatibility conditions on these orbits, we prove that one of these W-algebras can be obtained as…

We prove that the classical $W$-algebra associated to a nilpotent orbit in a simple Lie-algebra can be constructed by preforming bihamiltonian, Drinfeld-Sokolov or Dirac reductions. We conclude that the classical $W$-algebra depends only on…

Let $\mathfrak{g}$ be a simple Lie algebra: its dual space $\mathfrak{g}^*$ is a Poisson variety. It is well known that for each nilpotent element $f$ in $\mathfrak{g}$, it is possible to construct a new Poisson structure by Hamiltonian…

We introduce the notion of an asymptotic algebra of chiral differential operators. We then construct, via a chiral Hamiltonian reduction, one such algebra over a resolution of the intersection of the Slodowy slice with the nilpotent cone.…

First, we derive an explicit formula for the Poisson bracket of the classical finite W-algebra W^{fin}(g,f), the algebra of polynomial functions on the Slodowy slice associated to a simple Lie algebra g and its nilpotent element f. On the…