All Questions

Let $(W,S)$ be a finite Coxeter system. Let us consider the following situation: Let $v_1,v_2,w\in W$ such that $v_1=wv_2w^{-1}$. Let $s_{\beta_r}\ldots s_{\beta_1}$ be a reduced expression of $v_2$. ...

Let $W$ be the symmetric group on $n+1$ letters. Let $\ell$ be the length function on $W$. As the title says, can we characterize all $v\in W$ such that there exists a $w\in W$ such that for all ...