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pro vyhledávání: '"Bruhat order"'
Autor:
Nicolaides, Robert, Rowley, Peter
Suppose that $W$ is a finite Coxeter group and $W_J$ a standard parabolic subgroup of $W$. The main result proved here is that for any for any $w \in W$ and reduced expression of $w$ there is an Elnitsky tiling of a $2m$-polygon, where $m = [W : W_J]
Externí odkaz:
http://arxiv.org/abs/2407.07975
Autor:
Hebert, Auguste, Philippe, Paul
Let $G$ be a split Kac-Moody group over a local field. In their study of the Iwahori-Hecke algebra of $G$, A.Braverman, D. Kazhdan and M. Patnaik defined a partial order - called the affine Bruhat order - on the extended affine Weyl semi-group $W^+$
Externí odkaz:
http://arxiv.org/abs/2405.12559
Autor:
Ghebleh, Mohammad
Publikováno v:
Linear Algebra and its Applications, Volume 446, 1 April 2014, Pages 377-387
Let $\mathcal{A}(R,S)$ denote the class of all matrices of zeros and ones with row sum vector $R$ and column sum vector~$S$. We introduce the notion of an inversion in a $(0,1)$--matrix. This definition extends the standard notion of an inversion of
Externí odkaz:
http://arxiv.org/abs/2401.15431
Given a Coxeter group $W$ with Coxeter system $(W,S)$, where $S$ is finite. We provide a complete characterization of Boolean intervals in the weak order of $W$ uniformly for all Coxeter groups in terms of independent sets of the Coxeter graph. Moreo
Externí odkaz:
http://arxiv.org/abs/2403.07989
Autor:
Chapelier-Laget, Nathan, Gobet, Thomas
We study the restriction of the strong Bruhat order on an arbitrary Coxeter group $W$ to cosets $x W_L^\theta$, where $x$ is an element of $W$ and $W_L^\theta$ the subgroup of fixed points of an automorphism $\theta$ of order at most two of a standar
Externí odkaz:
http://arxiv.org/abs/2311.06827
The combinatorially and the geometrically defined partial orders on the set of permutations coincide. We extend this result to $(0,1)$-matrices with fixed row and column sums. Namely, the Bruhat order induced by the geometry of a Cherkis bow variety
Externí odkaz:
http://arxiv.org/abs/2311.05531
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The Bruhat order on a Coxeter group is often described by examining subexpressions of a reduced expression. We prove that an analogous description applies to the Bruhat order on double cosets. This establishes the compatibility of the Bruhat order on
Externí odkaz:
http://arxiv.org/abs/2307.15726