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 Y w , g , which is attached to an element w in the Weyl group of G L n and g ∈ G L n . The main theorem of this paper states that the Euler characteristic of Y w , 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 . [ABSTRACT FROM AUTHOR]