Elements of minimal length and Bruhat order on fixed point cosets of Coxeter groups

Nathan Chapelier-Laget, Thomas Gobet

We study the restriction of the strong Bruhat order on an arbitrary Coxeter group $W$ to cosets $x{W}_L^{\theta }$, where $x$ is an element of $W$ and $W_L^{\theta }$ the subgroup of fixed points o…