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] (which correspond to the case H = {1}), 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.
Partial and global representations of finite groups
Paolo Saracco;
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 [DEP00] (which correspond to the case H = {1}), 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.
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Open Access dal 24/05/2023
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