Cyclic sieving of finite Grassmannians and flag varieties

In this paper, we prove instances of the cyclic sieving phenomenon for finite Grassmannians and partial flag varieties, which carry the action of various tori in the finite general linear group GL n ( F q ) . The polynomials involved are sums of certain weights of the minimal length parabolic coset representatives of the symmetric group S n , where the weight of a coset representative can be written as a product over its inversions.