Centers and Azumaya loci of finite WW-algebras

In this paper, we study the center $Z$ of the finite $W$-algebra $\mathcal{T}(\mathfrak{g},e)$ associated with a semi-simple Lie algebra $\mathfrak{g}$ over an algebraically closed field \mathds{k} of characteristic $p\gg0$, and an arbitrarily given nilpotent element $e\in\mathfrak{g}$. We obtain an analogue of Veldkamp's theorem on the center. For the maximal spectrum $\text{Specm}(Z)$, we show that its Azumaya locus coincides with its smooth locus of smooth points. The former locus reflects irreducible representations of maximal dimension for $\mathcal{T}(\mathfrak{g},e)$.Comment: 31 page

Super Vust theorem and Schur-Sergeev duality for principal finite WW-superalgebras

In this paper, we first formulate a super version of Vust theorem associated with a regular nilpotent element $e\in\mathfrak{gl}(V)$. As an application of this theorem, we then obtain the Schur-Sergeev duality for principal finite $W$-superalgebras which is partially a super version of Brundan-Kleshchev's higher level Schur-Weyl duality.Comment: 35 pages, comments are welcom

On the Relationship Between Children’s Social Development and Their Class Conditions at Kindergarten in the Undeveloped Region

The research purpose is to know the relationship between children’s social development and the class-condition of kindergarten. Research methods are the questionnaire investigation and interview method. The class-condition of 54 classes is overall measured by questionnaire investigation for some preschool education group in Yanbian County of Sichuan province, in China. The social development of 30 children is known by observation and interview method in the same preschool education group. The obtained data is processed by SPSS.22 in the PC. The results of the study are that: (a) Most of the children’s social development is good, especially in the aspect of social interaction and self control; but most of the children have not still formed good habits. (b) Most of the classes in the kindergarten do well nurse in daily life, curriculum classes and children’s development evaluation; but there is shortage in the decorating wall among most of the classes in kindergarten. (c) It is analyzed by stepwise regression for the social development of children including each factor as the dependent variable and each factor among class-conditions of the kindergarten as the independent variable. The result shows that nursing in daily life and decorating wall entered the regression equation. It is clear that nursing in daily life and the decorating wall have important influence on children’s social development. The conclusions are that teachers should pay attention to the cultivation of the children’s good habits; that teachers should strengthen the decorating wall in class; that teachers should look at the class everyday life care as an important part of the job

Study on the Experiment of Cultivating the Peer Interpersonal Skill of the Children in the Kindergarten

This purpose of research is that cultivating the peer interpersonal skill of the children in the kindergarten of the linguistic& non-linguistic competence, pro-social behavior & social obstacle. Research methods are on-the-spot experimental and observational method. The results are that the difference is significance in the total level of the children’s peer interpersonal skill between the experimental group and the control group (p＜0.05), that the difference is significance in the linguistic & non-linguistic competence and the children’s interaction obstacle between the experimental group and the control group (p＜0.05). But that the difference is no significance in the social initiative and pro-social between the experimental group and the control group (p＞0.05). The conclusion is that it is effective for teachers to intervene in children’s peer interaction during the experiment. It can become the appropriate education measures to improve the peer interpersonal skill of the children in the kindergarten