"Bruhat ordering"의 두 판 사이의 차이

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-==introduction==
-* Let $W$ be a Coxeter group
-;def (Bruhat ordering)
-Define a partial order on the elements of $W$ as follows :
-Write $w'\xrightarrow{t} w$ whenever $w = w' t$ for some reflection $t$ and $\ell(w') < \ell(w)$. Define $w'<w$ if there is a sequence $w'=w_0\to w_1\to \cdots \to w_n=w$. Extend this relation to a partial ordering of $W$. (reflexive, antisymmetric, transitive)
-* example : http://groupprops.subwiki.org/wiki/File:Bruhatons3.png
-;thm
-Given $x,y\in W$, we have $x\le y$ in the Bruhat order if and only if there is a reduced expression $y=s_{i_1}s_{i_2}\cdots s_{i_k}$ such that $x$ can be written as a product of some of the $s_{i_j}$ in the same order as they appear in $y$.
-==history==
-* The Bruhat order on the Schubert varieties of a flag manifold or Grassmannian was first studied by Ehresmann (1934), and the analogue for more general semisimple algebraic groups was studied by Chevalley (1958).
-==memo==
-* See also Chapter 8 of Humphereys' 'Reflection groups and Coxeter groups'
-==related items==
-* [[Flag manifold and flag variety]]
-==computational resource==
-* https://drive.google.com/file/d/0B8XXo8Tve1cxdko1Z0hPZUNhZTQ/view
-* http://math.univ-lyon1.fr/homes-www/ducloux/coxeter/coxeter3/english/bruhat_e.html

2020년 11월 13일 (금) 03:07 판