Journal of East China Normal University(Natural Sc ›› 2016, Vol. 2016 ›› Issue (1): 27-38.doi: 10.3969/j.issn.1000-5641.2016.01.004

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Cells of the weighted Coxeter group (C3,l6)

YUE  Ming-Shi   

  • Received:2014-12-08 Online:2016-01-25 Published:2016-03-10

Abstract: Let \alpha be a group automorphism of the affine Weyl group (\widetilde{A}_{2n},\widetilde{S}) with \alpha(\widetilde{S})=\widetilde{S}. Affine Weyl group(\widetilde{C}_n,S) can be seen as the fixed point set of the affine Weyl group (\widetilde{A}_{2n},\widetilde{S}) under its group automorphism \alpha. 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 this paper, we
give the description for all the left and two-sided cells of the specific weighted Coxeter group (\widetilde{C}_3,\widetilde{l}_6) and prove that each left cell in (\widetilde{C}_3,\widetilde{l}_6) is left-connected.

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

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