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The absolute order on the hyperoctahedral group

Abstract : The absolute order on the hyperoctahedral group $B_n$ is investigated. It is shown that every closed interval in this order is shellable, those closed intervals which are lattices are characterized and their zeta polynomials are computed. Moreover, using the notion of strong constructibility, it is proved that the order ideal generated by the Coxeter elements of $B_n$ is homotopy Cohen-Macaulay and the Euler characteristic of the order complex of the proper part of this ideal is computed. Finally, an example of a non Cohen-Macaulay closed interval in the absolute order on the group $D_4$ is given and the closed intervals of $D_n$ which are lattices are characterized.
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Myrto Kallipoliti. The absolute order on the hyperoctahedral group. 21st International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2009), 2009, Hagenberg, Austria. pp.503-514. ⟨hal-01185381⟩

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