分野別セミナー

Given an odd prime number $p$ and a Coxeter group $W$ such that the order of the product $st$ is prime to $p$ for every Coxeter generators $s,t$ of $W$, we prove that the $p$-local homology groups $H_k(W,¥Zp)$ vanish for $1¥leq k¥leq 2(p-1)$. This generalize a known result for symmetric groups due to Nakaoka.