Zeta-functions of root systems and Poincaré polynomials of Weyl groups

Yasushi Komori, Kohji Matsumoto, Hirofumi Tsumura

We consider a certain linear combination $S(\mathbf{s},\mathbf{y};I;\Delta )$ of zeta-functions of root systems, where $\Delta$ is a root system of rank $r$ and $I\subset \{1,2,\dots ,r\}$. Sh…