The alternating subgroup of the colored permutation group

par David Garber (Holon Institute of Technology)

mardi 17 oct. 2017, 10:45 → 11:45 Europe/Paris

Bât. Braconnier, salle Fokko du Cloux (ICJ, Université Lyon 1)

The alternating subgroup of the colored permutation group is the natural analogue of the alternating group inside the wreath product (\mathbb{Z}_r \wr S_n\). We present a 'Coxeter like' presentation for this group and calculate the length function with respect to this presentation. Then, we present this group as covering of \(\mathbb{Z}_{\frac{r}{2}} \wr S_n\) and use this point of view to give another expression for the length function. We also apply this covering to lift a known parameter of \(\mathbb{Z}_{\frac{r}{2}} \wr S_n\) to the alternating colored permutation group. Based on a joint work with Eli Bagno and Toufik Mansour.