On the decomposition numbers of the Hecke algebra of type $D_n$ when $n$ is even

Jun Hu

Let $n\ge 4$ be an even integer. Let $K$ be a field with $\cha K\neq 2$ and $q$ an invertible element in $K$ such that ${\prod }_{i=1}^{n-1}(1+q^i)\ne 0$. In this paper, we study th…