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Partial and Global Representations of Finite Groups

par D'Adderio, Michele ;Hautekiet, William ;Saracco, Paolo ;Vercruysse, Joost
Référence Algebras and representation theory
Publication Publié, 2023-05-01

Article révisé par les pairs

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Résumé :

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 Sn and its subgroup Sn−1 of permutations fixing 1: this provides a natural extension of the classical representation theory of Sn.