Let $G$ be a reductive p-adic group. Let $W$ be a weyl group. if $w$, and $w_o \in W$. I want to know in which case we have $w w_o w^{-1}= w_o$ ?

in case if $y(\theta)=\theta $ where $\theta$ is a subset of simple roots, and $w$ is the longest element in $W_\theta$, the subgroup of $W$ generated by $s_\alpha$ (simple reflection of $\alpha$), where $\alpha$ is in $\theta$.

thanks.

Let $G$ be a reductive p-adic group. Let $W$ be a weyl group. if $w$, and $w_o \in W$. I want to know in which case we have $w w_o w^{-1}= w_o$ ?

in case if $w_o(\theta)=\theta $ where $\theta$ is a subset of simple roots, and $w$ is the longest element in $W_\theta$, the subgroup of $W$ generated by $s_\alpha$ (simple reflection of $\alpha$), where $\alpha$ is in $\theta$.

thanks.

Let G be a reductive p-adic group. Let W be a weyl group. if x,y in W I want to know in which case we have x y x^-1 = y ?

in case if y(θ)=θ where θ is a subset of simple roots, and x is the longest element in W_θ, the subgroup of W generated by s_α (simple reflection of α), where α is in θ.

thanks.

Let $G$ be a reductive p-adic group. Let $W$ be a weyl group. if $w$, and $w_o \in W$. I want to know in which case we have $w w_o w^{-1}= w_o$ ?

in case if $y(\theta)=\theta $ where $\theta$ is a subset of simple roots, and $w$ is the longest element in $W_\theta$, the subgroup of $W$ generated by $s_\alpha$ (simple reflection of $\alpha$), where $\alpha$ is in $\theta$.

thanks.