The branching-diagram conjecture for Richardson elements of type (b) symplectic parabolics

Let $\mathfrak{sp}_{2n}$ be the symplectic Lie algebra, and consider a parabolic subalgebra of type (b) with block parameters $d=(d_1,\ldots,d_r,d_{r+1},d_r,\ldots,d_1)$. Let $L_{odd}(d)$ denote the corresponding simple line diagram, and call a block length odd when $d_i$ is odd. A repetition of odd entries is a sequence $d_i=d_{i+1}=\dots=d_{i+s}$, with each repeated entry smaller than $d_{r+1}$. Branching-diagram conjecture. The diagram defining a Richardson element is obtained from $L_{odd}(d)$ by adding a branching for every repetition $d_i=d_{i+1}=\dots=d_{i+s}$ of odd entries smaller than $d_{r+1}$. The conjecture proposes a uniform diagrammatic construction for Richardson elements in this class of symplectic parabolic subalgebras, extending the simple line-diagram construction; the supplied text does not establish whether the construction is valid in general.