The Conformal Characters

Understand

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.