Generalized Green functions and unipotent classes for finite reductive groups, IV

In this paper, we formulate the notion of split elements of a unipotent class in a connected reductive group G. Generalized Green functions of G can be computed by using Lusztig's algorithm, if split elements exist for any unipotent class. The existence of split elements is reduced to the case where G is a simply connected, almost simple group. We show, in the case of classical groups, split elements exist, which is a refinement of previous results. In the case of exceptional groups, we show the existence of split elements, possibly except one class for G of type E₇.