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 Dokuchaev et al. (J. Algebra 226(1), 505–532, 2000) (which correspond to the case H = {1G}), we develop further an effective theory that allows explicit computations. As a case study, we apply our theory to the symmetric group $\mathfrak {S}_{n}$ and its subgroup $\mathfrak {S}_{n-1}$ of permutations fixing 1: this provides a natural extension of the classical representation theory of $\mathfrak {S}_{n}$ .