Character (mathematics)

About: Character (mathematics) is a research topic. Over the lifetime, 46723 publications have been published within this topic receiving 411412 citations.

The Logical problem of language acquisition

Abstract: This collection of articles and associated discussion papers focuses on a problem that has attracted increasing attention from linguists and psychologists throughout the world during the past several years. Reduced to essentials, the problem is that of discovering the character of the mental capacities that make it possible for human beings to attain knowledge of their language on the basis of fragmentary and haphazard early linguistic experience. A fundamental assumption running through all of these contributions is that people possess strong innate predispositions that are critical for success in this task.

The admissible dual of GL(N) via compact open subgroups

Abstract: This work gives a full description of a method for analyzing the admissible complex representations of the general linear group "G" = "Gl(N, F)" of a non-Archimedean local field "F" in terms of the structure of these representations when they are restricted to certain compact open subgroups of "G." The authors define a family of representations of these compact open subgroups, which they call "simple types." The first example of a simple type, the "trivial type," is the trivial character of an Iwahori subgroup of "G." The irreducible representations of "G" containing the trivial simple type are classified by the simple modules over a classical affine Hecke algebra. Via an isomorphism of Hecke algebras, this classification is transferred to the irreducible representations of "G" containing a given simple type. This leads to a complete classification of the irreduc-ible smooth representations of "G," including an explicit description of the supercuspidal representations as induced representations. A special feature of this work is its virtually complete reliance on algebraic methods of a ring-theoretic kind. A full and accessible account of these methods is given here.