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The boundedness of the weighted Coxeter group with complete graph


Authors: Jian-yi Shi and Gao Yang
Journal: Proc. Amer. Math. Soc. 144 (2016), 4573-4581
MSC (2010): Primary 20F55
DOI: https://doi.org/10.1090/proc/13154
Published electronically: July 7, 2016
MathSciNet review: 3544509
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Abstract: We prove that a weighted Coxeter group $ (W,S,L)$ is bounded with $ \mathbf {a}(W)=\mathbf {b}'(W):=\max \{L(u),L(w_{s,t})\mid u,s,t\in S,\vert W_{s,t}\vert<\infty \}$ if the Coxeter graph of $ W$ is complete and $ \mathbf {b}'(W)<\infty $, where $ W_{s,t}$ is the parabolic subgroup of $ W$ generated by $ s\ne t$ in $ S$ and $ w_{s,t}$ is the longest element in $ W_{s,t}$ whenever $ W_{s,t}$ is finite.


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Additional Information

Jian-yi Shi
Affiliation: Department of Mathematics, East China Normal University, Shanghai, 200241, People’s Republic of China

Gao Yang
Affiliation: Department of Mathematics, East China Normal University, Shanghai, 200241, People’s Republic of China

DOI: https://doi.org/10.1090/proc/13154
Keywords: Weighted Coxeter group, complete graph, $\mathbf{a}$-function, boundedness
Received by editor(s): March 21, 2015
Published electronically: July 7, 2016
Additional Notes: This research was supported by the NSF of China (11131001 and 11471115), Shanghai Key Laboratory of PMMP, and STCSM (13dz2260400)
Dedicated: Dedicated to Professor George Lusztig on his 70th birthday.
Communicated by: Pham Huu Tiep
Article copyright: © Copyright 2016 American Mathematical Society