On the automorphism groups of complex homogeneous spaces

有限根树自同构群的表示论

Representation theory of the group of automorphisms of a finite rooted tree

本研究构造了有限根树自同构群的常不可约表示并实现天然参数化，通过引入树合成组合学导出对应置换表示，方法适用于非球对称树且无坐标依赖。

A classification of homogeneous operators in the Cowen-Douglas class

A complete list of homogeneous operators in the Cowen-Douglas class $B_n(D)$ is given. This classification is obtained from an explicit realization of all the homogeneous Hermitian holomorphic vector bundles on the unit disc under the action of the universal covering group of the bi-holomorphic automorphism group of the unit disc.

Local and 2-local derivations and automorphisms on simple Leibniz algebras

The present paper is devoted to local and 2-local derivations and automorphism of complex finite-dimensional simple Leibniz algebras. We prove that all local derivations and 2-local derivations on a finite-dimensional complex simple Leibniz algebra are automatically derivations. We show that nilpotent Leibniz algebras as a rule admit local derivations and 2-local derivations which are not derivations. Further we consider automorphisms of simple Leibniz algebras. We prove that every 2-local automorphism on a complex finite-dimensional simple Leibniz algebra is an automorphism and show that nilp…

群的复表示及其自同构的对合

Complex Representations of Groups and Involutions of its Automorphisms

本文建立了不可约特征标次数和与有限群自同构相关的扭曲对合数之间的关系，并开发了内自同构和对称群情形下的算法框架，进而给出了识别群具有复（非实）不可约表示的条件并探讨了结构推论。