The Conformal Characters

We revisit the study of the multiplets of the conformal algebra in any dimension. The theory of highest weight representations is reviewed in the context of the Bernstein-Gelfand-Gelfand category of modules. The Kazhdan-Lusztig polynomials code the relation between the Verma modules and the irreducible modules in the category and are the key to the characters of the conformal multiplets (whether finite dimensional, infinite dimensional, unitary or non-unitary). We discuss the representation theory and review in full generality which representations are unitarizable. The mathematical theory that allows for both the general treatment of characters and the full analysis of unitarity is made accessible. A good understanding of the mathematics of conformal multiplets renders the treatment of all highest weight representations in any dimension uniform, and provides an overarching comprehension of case-by-case results. Unitary highest weight representations and their characters are classified and computed in terms of data associated to cosets of the Weyl group of the conformal algebra. An executive summary is provided, as well as look-up tables up to and including rank four.Comment: 41 pages, many figure

Individuation in the Main Characters of J.K. Rowling's HARRY POTTER Series

This paper examines the individuation of Potter and Voldemort in Harry Potter series. To be a holistic individual, a person needs to be individuated by managing their three main archetypes. The three main archetypes are persona, shadow, and anima or animus. Potter and Voldemort have to manage their archetypes their journey as human beings. Each of them has to know his persona including his appearance, behavior and role; confront his shadow; and balance his anima. In the end, Potter manages himself to be a individuated person who can lead a good life, while Voldemort fails to be an individuated person and, as a result, he died