Simplicity of vacuum modules and associated varieties

Simplicity of vacuum modules over affine Lie superalgebras

We prove an explicit condition on the level $k$ for the irreducibility of a vacuum module $V^{k}$ over a (non-twisted) affine Lie superalgebra, which was conjectured by M. Gorelik and V.G. Kac. An immediate consequence of this work is the simplicity conditions for the corresponding minimal W-algebras obtained via quantum reduction, in all cases except when the level $k$ is a non-negative integer.

On simplicity and stability of tangent bundles of rational homogeneous varieties

Given a rational homogeneous variety G/P where G is complex simple and of type ADE, we prove that all tangent bundles T_{G/P} are simple, meaning that their only endomorphisms are scalar multiples of the identity. This result combined with Hitchin-Kobayashi correspondence implies stability of these tangent bundles with respect to the anticanonical polarization. Our main tool is the equivalence of categories between homogeneous vector bundles on G/P and finite dimensional representations of a given quiver with relations.

关于泛最小W-代数的单性

On simplicity of universal minimal W-algebras

本文研究泛最小量子仿射W-代数的单性，并应用此结果确定超共形代数真空模不可约时的中心取值。

Representations of Lie algebras of vector fields on affine varieties

For an irreducible affine variety $X$ over an algebraically closed field of characteristic zero we define two new classes of modules over the Lie algebra of vector fields on $X$ - gauge modules and Rudakov modules, which admit a compatible action of the algebra of functions. Gauge modules are generalizations of modules of tensor densities whose construction was inspired by non-abelian gauge theory. Rudakov modules are generalizations of a family of induced modules over the Lie algebra of derivations of a polynomial ring studied by Rudakov. We prove general simplicity theorems for these two typ…

费米子扩展的W-代数 via 3d N=4 超对称 gauge 理论与边界

Fermionic extensions of $W$-algebras via 3d $\mathcal{N}=4$ gauge theories with a boundary

研究3d H-twisted N=4超对称 gauge 理论与边界相关的顶点算子代数性质，发现其为费米子扩展的W-代数。