On quotients of Hom-functors and representations of finite general linear groups, I

Abstract

Abstract This is a second article on quotients of Hom-functors and their applications to the representation theory of finite general linear groups in a nondescribing characteristic. After some general results on quotients of Hom-functors and their connection to the Harish–Chandra theory these constructions are used to obtain a full classification of the l-modular irreducible representations of GL n ( q ) for some prime power q which is not divisible by the prime l and to explain some facts on their Harish–Chandra series and decomposition numbers.