A subalgebra of 0-Hecke algebra

Xuhua He

Group Theory and Lie Theory mathscidoc:1912.43204

Journal of Algebra, 322, (11), 4030-4039
Let (W, I) be a finite Coxeter group. In the case where W is a Weyl group, Berenstein and Kazhdan in [A. Berenstein, D. Kazhdan, Geometric and unipotent crystals. II. From unipotent bicrystals to crystal bases, in: Quantum Groups, in: Contemp. Math., vol. 433, Amer. Math. Soc., Providence, RI, 2007, pp. 1388] constructed a monoid structure on the set of all subsets of I using unipotent -linear bicrystals. In this paper, we will generalize this result to all types of finite Coxeter groups (including non-crystallographic types). Our approach is more elementary, based on some combinatorics of Coxeter groups. Moreover, we will calculate this monoid structure explicitly for each type.
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  title={A subalgebra of 0-Hecke algebra},
  author={Xuhua He},
  booktitle={Journal of Algebra},
Xuhua He. A subalgebra of 0-Hecke algebra. Vol. 322. In Journal of Algebra. pp.4030-4039. http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20191221112926029284764.
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