Generalized exponents of small representations. I

This is the first paper in a sequence devoted to giving manifestly non-negative formulas for generalized exponents of small representations in all types. The main part of this paper illustrates the overall structure of the argument on root systems of type A and discusses the relationship with the Lascoux-Schutzenberger charge formula.Comment: 30 p

BGG reciprocity for current algebras

It was conjectured by Bennett, Chari, and Manning that a BGG-type reciprocity holds for the category of graded representations with finite-dimensional graded components for the current algebra associated to a simple Lie algebra. We associate a current algebra to any indecomposable affine Lie algebra and show that, in this generality, the BGG reciprocity is true for the corresponding category of representations.Comment: 23 pg, corrections to Lemma 2.1

Testing the Application for Analyzing Structured Entities

The paper presents the testing process of the application for the analysis of structured text entities. The structured entities are presented. Quality characteristics of structured entities are identified and analyzed. The design and building processes are presented. Rules for building structured entities are described. The steps of building the application for the analysis of structured text entities are presented. The objective of the testing process is defined. Ways of testing the application on components and as a whole are established. A testing strategy for different objectives is proposed. The behavior of users during the testing period is analyzed. Statistical analysis regarding the behavior of users in processes of infinite resources access are realized.Structured Entity, Application, Analysis, Testing, Metrics