Journal of East China Normal University(Natural Science) >

2015 , Vol. 2015 >Issue 3: 38 - 46

DOI: https://doi.org/10.3969/j.issn.1000-5641.2015.03.006

Article

Cells of the weighted Coxeter group Cn

  • YUE Ming-Shi
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Received date: 2014-08-07

  Online published: 2015-05-28

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Abstract

Affine Weyl group (widetilde{C}_n,S) can be seen as a fixed point set of the affine Weyl group (widetilde{A}_{2n},widetilde{S}) under a certain group
automorphism alpha of widetilde{A}_{2n} with alpha(widetilde{S})=widetilde{S}. Let widetilde{l} be the length function on widetilde{A}_{2n}. The restriction to
widetilde{C}_n of widetilde{l} on widetilde{A}_{2n} can be seen as a weight function on widetilde{C}_n. In this paper, by studying the fixed point set of the affine Weyl group widetilde{A}_{2n} under alpha, we can give the description of all the cells of weighted Coxeter group (widetilde{C}_n,widetilde{l}) corresponding to the partition bf{2^{n-1}1^3}.

Key words： affine Weyl group; quad weighted Coxetergroup; quad quasi-split case; quad partitions of the positive integer n; quad left cells; quad two-sided cells

Cite this article

YUE Ming-Shi . Cells of the weighted Coxeter group Cn[J]. Journal of East China Normal University(Natural Science), 2015 , 2015(3) : 38 -46 . DOI: 10.3969/j.issn.1000-5641.2015.03.006

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