e-mail: mimachi@math.kyushu-u.ac.jp

**A representation of the Iwahori-Hecke algebra on the
twisted homology associated with the Selberg type integral**

**Abstract**

We consider the twisted cycle (an element of the homology with the local
system coefficient) defined by the integrand of the Selberg type integral.
When we choose an appropriate subspace of it, we can construct a representation
of the Iwahori-Hecke algebra.