More on the Terwilliger algebra of Johnson schemes

In [F. Levstein, C. Maldonado, The Terwilliger algebra of the Johnson schemes, Discrete Math. 307 (2007) 1621–1635], the Terwilliger algebra of the Johnson scheme $J(n,d)$ was determined when $n\ge 3d$. In this paper, we determine the Terwilliger algebra $\mathcal{T}$ for the remaining case $2d\leq n<3d$.