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A Coxeter group is a group defined by a presentation by involutions $r_i$ with relators $(r_ir_j)^{m_{ij}}=1$ for certain family $(m_{ij})$ of integers greater than 1.

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coset poset of reflection subgroup

Fix a finitely generated Coxeter system $(W, S)$, and let $W_J$ denote the standard parabolic proper subgroup generated by a subset $J \subset S$. It is well known that the poset of cosets $\{xW_J\}$ …
J.D.Chern's user avatar