The boundedness of the weighted Coxeter group with complete graph
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- by Jian-yi Shi and Gao Yang
- Proc. Amer. Math. Soc. 144 (2016), 4573-4581
- DOI: https://doi.org/10.1090/proc/13154
- Published electronically: July 7, 2016
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Abstract:
We prove that a weighted Coxeter group $(W,S,L)$ is bounded with $\mathbf {a}(W)=\mathbf {b}’(W):=\max \{L(u),L(w_{s,t})\mid u,s,t\in S,|W_{s,t}|<\infty \}$ 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.References
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Bibliographic Information
- Jian-yi Shi
- Affiliation: Department of Mathematics, East China Normal University, Shanghai, 200241, People’s Republic of China
- MR Author ID: 231063
- Gao Yang
- Affiliation: Department of Mathematics, East China Normal University, Shanghai, 200241, People’s Republic of China
- 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)
- Communicated by: Pham Huu Tiep
- © Copyright 2016 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 144 (2016), 4573-4581
- MSC (2010): Primary 20F55
- DOI: https://doi.org/10.1090/proc/13154
- MathSciNet review: 3544509
Dedicated: Dedicated to Professor George Lusztig on his 70th birthday.