Journal of East China Normal University(Natural Science) >

2016 , Vol. 2016 >Issue 4: 1 - 10

DOI: https://doi.org/10.3969/j.issn.1000-5641.2016.04.001

Cells of the weighted Coxeter group\\ $\textbf{(}\widetilde{\bm C}_{\bm n},\widetilde{\bm l}_{\textbf{2}\bm n}\textbf{)}$ in a certain quasi-split case

  • YUE Ming-shi
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  • School of Logistics, Linyi University, Linyi Shandong 276000, China

Received date: 2015-05-27

  Online published: 2016-09-29

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Abstract

The fixed point set of the affine Weyl group $(\widetilde{A}_{2n},\widetilde{S})$ under its group automorphism $\alpha$ with $\alpha(\widetilde{S})=\widetilde{S}$ can be seen as the affine Weyl group $(\widetilde{C}_n,S)$. The restriction to $\widetilde{C}_{n}$ of the length function $\widetilde{l}_{2n}$ on $\widetilde{A}_{2n}$ can be seen as a weight function on $\widetilde{C}_{n}$. In the present paper, by studying the fixed point set of the affine Weyl group $(\widetilde{A}_{2n},\widetilde{S})$ under $\alpha$, we give the description for all the cells of the weighted Coxeter group $(\widetilde{C}_{n},\widetilde{l}_{2n})$ corresponding to the specific partition $\bf{3^32^{n-4}}$. We also prove that each left cell we considered in this paper is left-connected, verifying a conjecture of Lusztig in our case.

Key words： affine Weyl group; weighted Coxeter group; left cells ; quasi-split case ; partitions of n

Cite this article

YUE Ming-shi . Cells of the weighted Coxeter group\\ $\textbf{(}\widetilde{\bm C}_{\bm n},\widetilde{\bm l}_{\textbf{2}\bm n}\textbf{)}$ in a certain quasi-split case[J]. Journal of East China Normal University(Natural Science), 2016 , 2016(4) : 1 -10 . DOI: 10.3969/j.issn.1000-5641.2016.04.001

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