Coxeter群上的Bruhat序与Bruhat区间的基数
发布时间：2019-03-20 08:40
【摘要】：Coxeter群在代数,几何,组合学和其它数学领域都有重要应用。在很多地方都用了代数和几何观点来阐述Coxeter群理论。这篇文章的主要目的是研究XYXsY,XYZ XsYtZ成立的条件和Bruhat区间的基数。在第一章中,我们简要介绍了一些关于反射群和Coxeter群的相关概念,定义和命题,如长度函数、Bruhat序、子表达等。在第二章中,我们得首先到了XYXsY充要条件是要么s(?)R(X)∪￡(Y),要么s∈R(X)∩￡(Y)(见推论2.1.8);其次,在一定的条件下通过Coxeter变换我们可以得到XYZXsYtZ(见命题2.2.7)。在第三章中,设W(Nn和Hn的一个半直积)是Bn型Coxeter群。设w1,w2 ∈ ,令w1=w'1u1,w2= w'2u1,其中w'1,w'2∈Nn,u1,u2∈An-1。若w1 ≤ w2在Wn 中成立,则 w'1 ≤ w2'在Nn中成立(见第三章命题3.2.5)。在第四章中,我们主要讨论了Bruhat区间的基数(C[w1,w2])。通过讨论s是否在R(w1)中,w1 ≤ w2s或w1(?)w2s,我们得到了C[w1, w2]和C[w1,w2s],C[w1s,w2s], 者之间的关系(主要见命题4.1.6到命题4.1.9)。
[Abstract]:Coxeter groups have important applications in algebra, geometry, combinatorial science and other mathematical fields. In many places, algebra and geometry are used to explain Coxeter group theory. The main purpose of this paper is to study the conditions under which XYXsY,XYZ XsYtZ holds and the cardinality of Bruhat intervals. In the first chapter, we briefly introduce some related concepts, definitions and propositions about reflection group and Coxeter group, such as length function, Bruhat order, subexpression and so on. In the second chapter, we first get to the XYXsY if and only if either s (?) R (X) / (Y), or s / R (X) / (Y) (see corollary 2.1.8); Secondly, we can get XYZXsYtZ by Coxeter transformation under certain conditions (see Proposition 2.2.7). In Chapter 3, let W (Nn and Hn be a semi-direct product of type B n Coxeter group. Let W _ 1, W _ 2 鈭，
本文编号：2444041
[Abstract]:Coxeter groups have important applications in algebra, geometry, combinatorial science and other mathematical fields. In many places, algebra and geometry are used to explain Coxeter group theory. The main purpose of this paper is to study the conditions under which XYXsY,XYZ XsYtZ holds and the cardinality of Bruhat intervals. In the first chapter, we briefly introduce some related concepts, definitions and propositions about reflection group and Coxeter group, such as length function, Bruhat order, subexpression and so on. In the second chapter, we first get to the XYXsY if and only if either s (?) R (X) / (Y), or s / R (X) / (Y) (see corollary 2.1.8); Secondly, we can get XYZXsYtZ by Coxeter transformation under certain conditions (see Proposition 2.2.7). In Chapter 3, let W (Nn and Hn be a semi-direct product of type B n Coxeter group. Let W _ 1, W _ 2 鈭，
本文编号：2444041
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