Quotient sheaves of algebraic supergroups are superschemes

On quotients of affine superschemes over finite supergroups

In this article we consider sheaf quotients of affine superschemes by finite supergroups that act on them freely. More precisely, if a finite supergroup $G$ acts on an affine superscheme $X$ freely, then the quotient $K$-sheaf $\tilde{X/G}$ is again an affine superscheme $Y$, where $K[Y]\simeq K[X]^G$. Besides, $K[X]$ is a finitely presented projective $K[X]^G$-module.

仿射群超概形的不可约表示及其自同态除超代数的分类

Classification of irreducible representations of affine group superschemes and the division superalgebras of their endomorphisms

本文在特征不为2的域上，基于可分闭包上的表示及其Galois扭转，分类了仿射群超概形的不可约表示，计算了其自同态的除超代数，并利用Shibata的Borel--Weil理论给出了特定条件下拟约化代数超群的数值结论。

Affine quotients of supergroups

In this article we consider sheaf quotients of affine superschemes by affine supergroups that act on them freely. The necessary and sufficient conditions for such quotients to be affine are given. If $G$ is an affine supergroup and $H$ is its normal supersubgroup, then we prove that a dur $K$-sheaf $\tilde{\tilde{G/H}}$ is again affine supergroup. Additionally, if $G$ is algebraic, then a $K$-sheaf $\tilde{G/H}$ is also algebraic supergroup and it coincides with $\tilde{\tilde{G/H}}$. In particular, any normal supersubgroup of an affine supergroup is faithfully exact.

仿射超概形的几何不变量理论

Geometric Invariant Theory for Affine Superschemes

本文为仿射超概形在约化代数超群作用下发展几何不变量理论，构造仿射超商，证明超几何希尔伯特-芒福德判据，并展示其用于构造GIT超商及与经典情形的差异。

Diagrams for perverse sheaves on isotropic Grassmannians and the supergroup SOSP(m|2n)

We describe diagrammatically a positively graded Koszul algebra \mathbb{D}_k such that the category of finite dimensional \mathbb{D}_k-modules is equivalent to the category of perverse sheaves on the isotropic Grassmannian of type D_k constructible with respect to the Schubert stratification. The connection is given by an explicit isomorphism to the endomorphism algebra of a projective generator described in by Braden. The algebra is obtained by a "folding" procedure from the generalized Khovanov arc algebras. We relate this algebra to the category of finite dimensional representations of the …

基本准可约根数据与超群

Basic quasi-reductive root data and supergroups

本文研究了何时配对(G,Y)对应于准可约代数超群G，通过证明在特定条件下存在性和唯一性定理，给出了基本准可约超群的结构分类。