Elements with finite Coxeter part in an affine Weyl group

Xuhua He Zhongwei Yang

Representation Theory mathscidoc:1912.43225

Journal of Algebra, 372, 204-210, 2012.12
Let W a be an affine Weyl group and : W a W 0 be the natural projection to the corresponding finite Weyl group. We say that w W a has finite Coxeter part if (w) is conjugate to a Coxeter element of W 0. The elements with finite Coxeter part are a union of conjugacy classes of W a. We show that for each conjugacy class O of W a with finite Coxeter part there exists a unique maximal proper parabolic subgroup W J of W a, such that the set of minimal length elements in O is exactly the set of Coxeter elements in W J. Similar results hold for twisted conjugacy classes.
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@inproceedings{xuhua2012elements,
  title={Elements with finite Coxeter part in an affine Weyl group},
  author={Xuhua He, and Zhongwei Yang},
  url={http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20191221113039833138785},
  booktitle={Journal of Algebra},
  volume={372},
  pages={204-210},
  year={2012},
}
Xuhua He, and Zhongwei Yang. Elements with finite Coxeter part in an affine Weyl group. 2012. Vol. 372. In Journal of Algebra. pp.204-210. http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20191221113039833138785.
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