Cells of the weighted Coxeter group (B3, ?)

doi:10.3969/j.issn.1000-5641.2015.01.004

Abstract

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,
two-sided-connected).

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

CLC Number:

MI Qian-Qian, SHI Jian-Yi. Cells of the weighted Coxeter group (B₃, ?)[J]. Journal of East China Normal University(Natural Sc, 2015, 2015(1): 27-41.

References

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Cells of the weighted Coxeter group (B₃, ?)

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