A subalgebra of 0-Hecke algebra

الأصل · EN

Let (W, I) be a finite Coxeter group. In the case where W is a Weyl group, Berenstein and Kazhdan in BK constructed a monoid structure on the set of all subsets of I using unipotent χ-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.