  An etale cohomology group $W$ of some irreducible components, which is the
smooth compactification of an affine curve
$(X^{q^2}-X)^{q-1}=(Y^{q(q+1)}-Y^{q+1})^{q-1},$ in the stable reduction the
Lubin-Tate curve of level two is related to the Lusztig theory over finite
rings. In this paper, we investigate a relationship between the cohomology
group $W$ and the Lusztig theory.
