Representations of the group GL(n, F), where F is a local non-Archimedean local field: ПРЕДСТАВЛЕНИЯ ГРУППЫ GL(n, F), ГДЕ F - ЛОКАЛЬНОЕ НЕАРХИМЕДОВО ПОЛЕ

This article is a survey of recent results in the theory of representations of reductive ℘-adic groups. For simplicity of presentation only the groups GL(n) are treated. Chapter I provides general information on representations of locally compact zero-dimensional groups. Chapter II presents Harish-Chandra's method of studying the representations of GL(n), which is based on reduction to cuspidal representations. Some finiteness theorems are proved by this method. In Chapter III we study another approach to the representations of GL(n), due to Gel'fand and Kazhdan; it is based on restricting the representations from GL(n) to a subgroup Pn. All theorems are presented with detailed proofs. No prior information is assumed on the part of the reader except the most elementary familiarity with the structure of non-Archimedean local fields.