本文關(guān)鍵詞： 正特征 辛與正交冪零軌道閉包正規(guī)性 W-代數(shù) Vust定理 仿射辮子代數(shù) 高階Schur-Weyl對(duì)偶　出處：《華東師范大學(xué)》2017年博士論文　論文類型：學(xué)位論文

【摘要】：本論文由兩章構(gòu)成.在第一章我們研究正特征代數(shù)閉域上正交與辛型冪零軌道閉包的正規(guī)性.我們證明不包含d與e型不可約極小退化的冪零軌道閉包是正規(guī)的.相反包含e型極小不可約退化的冪零軌道閉包不正規(guī).這里,極小不可約退化是Hesselink在[Hes]中給出的,一共有8種參見表1.1.我們的結(jié)果是復(fù)數(shù)域上的結(jié)果[KP2,定理16.2(ii)]在正特征域上較弱一點(diǎn)的版本.我們采用的證明方法是[KP2]中的Kraft-Procesi論證,在正特征情形中需要更具體地實(shí)現(xiàn)一些過程.這一章的結(jié)果包含在已發(fā)表的論文[XS]中.作為冪零軌道閉包正規(guī)性的一個(gè)有趣應(yīng)用,在第二章我們給出B,C和D型的Vust定理,然后用Vust定理研究高階Schur-Weyl對(duì)偶.令G為復(fù)數(shù)域上的線性代數(shù)群,g=Lie(G)為其李代數(shù),e ∈ g為一冪零元.若G = GL(V),Ge(?)G為冪零元e的穩(wěn)定化子,Vust定理是說交換化代數(shù)EndGe,(V(?)d)由d次對(duì)稱群的自然作用的像和所有形如{1(?)(i-1)(?)e(?)1(?)(d-i)|i=1,…,d}的線性變換生成.在本文第二章,我們把這個(gè)定理推廣到G = O(V)和SP(V),此時(shí)我們需要限制條件冪零軌道閉包G·e是正規(guī)的.作為Vust定理的應(yīng)用我們研究B,C和D型的高階Schur-Weyl對(duì)偶,即建立有限W代數(shù)和退化仿射辮子代數(shù)之間的聯(lián)系.第二章基于已發(fā)表的[LX].
[Abstract]:In chapter 1, we study the normality of nilpotent orbital closures of orthogonal and symplectic type on closed fields of positive characteristic algebras. We prove that nilpotent orbital closures without d and e type irreducible minimal degeneracy are normal. Instead, the closure of nilpotent orbits containing minimal irreducible degeneracy of type e is irregular. Minimal irreducible degeneracy is given by Hesselink in [Hes], and there are eight kinds of results given in [Hes]. Our result is a weaker version of the result [KP2, Theorem 16.2ii] on complex field in [Hes]. Our proof method is the Kraft-Procesi proof in [KP2]. In the case of positive features, some processes need to be realized more concretely. The results of this chapter are contained in the published paper [XS]. As an interesting application of nilpotent orbital closure normality, in chapter 2 we give Vust theorems of BG C and D type. Then the Vust theorem is used to study the duality of higher order Schur-Weyl. Let G be a linear algebraic group G over the complex field. Let G be its lie algebra G 鈭，

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