Euler characteristic of analogues of a Deligne-Lusztig variety for GLn

We give a combinatorial formula to calculate the Euler characteristic of an analogue of a Deligne-Lusztig variety, denoted Yw,g, which is attached to an element w in the Weyl group of GLn and g∈GLn. The main theorem of this paper states that the Euler characteristic of Yw,g only depends on the unipotent part of the Jordan decomposition of g and the conjugacy class of w. It generalizes the formula of the Euler characteristic of Springer fibers for type A.