Journal of East China Normal University(Natural Sc ›› 2015, Vol. 2015 ›› Issue (1): 27-41.doi: 10.3969/j.issn.1000-5641.2015.01.004

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Cells of the weighted Coxeter group (B3, ?)

 MI  Qian-Qian1, SHI  Jian-Yi2   

  • Received:2013-12-01 Online:2015-01-25 Published:2015-03-29

Abstract: The affine Coxeter group ( e B3, S) can be realized as the fixed point set of the
affine Coxeter group ( e D4, eS) under a certain group automorphism α with α( eS) = eS. Let
e? be the length function of e D4. We gave an explicit description for all the left cells of the
weighted Coxeter group ( e B3, e?). Also§we showed that in the the weighted Coxeter groups
( e D4, e?) and ( e B3, e?), each left (respectively, two-sided) cell was left-connected (respectively,

Key words: weighted Coxeter group, quasi-split case, cells, left-connectedness

CLC Number: