  For a compact Poisson-Lie group $K$, the homogeneous space $K/T$ carries a
family of symplectic forms $\omega_\xi^s$, where $\xi \in \mathfrak{t}^*_+$ is
in the positive Weyl chamber and $s \in \mathbb{R}$. The symplectic form
$\omega_\xi^0$ is identified with the natural $K$-invariant symplectic form on
the $K$ coadjoint orbit corresponding to $\xi$. The cohomology class of
$\omega_\xi^s$ is independent of $s$ for a fixed value of $\xi$.
  In this paper, we show that as $s\to -\infty$, the symplectic volume of
$\omega_\xi^s$ concentrates in arbitrarily small neighbourhoods of the smallest
Schubert cell in $K/T \cong G/B$. This strengthens earlier results [9,10] and
is a step towards a conjectured construction of global action-angle coordinates
on $Lie(K)^*$ [4, Conjecture 1.1].
