Related papers: Symplectic resolutions for nilpotent orbits (II)

Let G be a connected linear semisimple Lie group with Lie algebra g, and let K_C --> Aut(p_C) be the complexified isotropy representation at the identity coset of the corresponding symmetric space G/K. Suppose that O is a nilpotent G-orbit…

In the classification of stationary solutions in extended supergravities with symmetric scalar manifolds, the nilpotent orbits of a real symmetric pair play an important role. In this paper we discuss two approaches to determining the…

The general solution of the graded contraction equations for a $\zz_2^{\otimes N}$ grading of the real compact simple Lie algebra $so(N+1)$ is presented in an explicit way. It turns out to depend on $2^N-1$ independent real parameters. The…

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…

We construct a Springer-type resolution of singularities of the odd nilpotent cone of the orthosymplectic Lie superalgebras osp(m|2n).

This is a continuation of math.AG/0609741. Let Y be an affine symplectic variety with a C^*-action with positive weights, and let \pi: X -> Y be its crepant resolution. Then \pi induces a natural map PDef(X) -> PDef(Y) of Kuranishi spaces…

We consider aspects of the geometry and topology of nilpotent orbits in finite-dimensional complex simple Lie algebras. In particular, we give the equivariant cohomologies of the regular and minimal nilpotent orbits with respect to the…

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…

It is well known that a symplectic Lie algebra admit a left symmetric product. In this work, we study the case where this product is Novikov, we show that the left-symmetric product associated to the symplectic Lie algrbra is Novikov if and…

We verify a conjecture of Beem and the first author stating that a certain family of physically motivated BRST reductions of beta-gamma systems and free fermions is isomorphic to $L_1(\mathfrak{psl}_{n|n})$, and that its associated variety…

The present work studies deeply quadratic symplectic Lie superalgebras, obtaining, in particular, that they are all nilpotent. Consequently, we provide classifications in low dimensions and identify the double extensions that maintain…

We consider canonical symplectic structure on the moduli space of flat ${\g}$-connections on a Riemann surface of genus $g$ with $n$ marked points. For ${\g}$ being a semisimple Lie algebra we obtain an explicit efficient formula for this…

We study symplectic structures on filiform Lie algebras -- nilpotent Lie algebras of the maximal length of the descending central sequence. In the present article we classify the Lie algebras with the structure relations of the following…

In this paper we describe the number of multiplicity-free primitive ideals associated with the rigid nilpotent orbits in finite-dimensional simple Lie algebras. Thanks to the results obtained earlier we need to solve the problem for the two…

The intersection cohomologies of closures of nilpotent orbits of linear (respectively, cyclic) quivers are known to be described by Kazhdan-Lusztig polynomials for the symmetric group (respectively, the affine symmetric group). We explain…

We treat the topic of the closures of the nilpotent orbits of the Lie algebras of Exceptional groups through their descriptions as moduli spaces, in terms of Hilbert series and the highest weight generating functions for their…

The projectivised nilpotent orbit closure P(\bar{O}) carries a natural contact structure on its smooth part. A resolution X \to P(\bar{O}) is called contact if the contact structure on P(O) extends to a contact structure on X. It turns out…

We study symplectic resolutions of the Hilbert scheme of two points on a surface with one ADE-singularity. We also characterize such singularities by central fibers of their symplectic resolutions. As an application, we show that these…

Let G = Sp (2n) be the symplectic group over Z. We present a certain kind of deformation of the nilpotent cone of G with G-action. This enables us to make direct links between the Springer correspondence of sp_{2n} over C, that over…

The Springer resolution of the nilpotent cone of a semisimple Lie algebra has played an important role in representation theory. The nilpotent cone is equal to Spec R, where R is the ring of regular functions on the nilpotent cone. This…