Partial and global representations of finite groups

Abstract: Given a subgroup H of a finite group G, we begin a systematic study of the partial representations of G that restrict to global representations of H. After adapting several results from DEP00, we develop further an effective theory that allows explicit computations. As a case study, we apply our theory to the symmetric group and its subgroup of permutations fixing 1: this provides a natural extension of the classical representation theory of the symmetric group.