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 = {1(G)}), we develop further an effective theory that allows explicit computations. As a case study, we apply our theory to the symmetric group S-n and its subgroup Sn-1 of permutations fixing 1: this provides a natural extension of the classical representation theory of S-n.
Partial and Global Representations of Finite Groups
D'Adderio M.;
2023-01-01
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 = {1(G)}), we develop further an effective theory that allows explicit computations. As a case study, we apply our theory to the symmetric group S-n and its subgroup Sn-1 of permutations fixing 1: this provides a natural extension of the classical representation theory of S-n.File in questo prodotto:
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