Green correspondence and its generalisations

In this paper, we investigate possible ways of generalising Green correspon dence, an important result of local representation theory. We introduce map s generalising Green correspondence: one from a group to one of its subgrou ps and another one from the subgroup to the group. Both are given in terms of restriction and induction. Through the first map, we get a new character isation of Green correspondence while the second one is a genuine generalis ation.