Factorizations in the irreducible characters of compact semisimple Lie groups

Our goal is to describe factorizations of the characters of irreducible representations of compact semisimple Lie groups. It is well-known that for a given Lie group G of rank n, the Virtual Representation Ring ℜ(G) with the operations of ⊗, ⊕, and [special characters omitted], is isomorphic to a polynomial ring with integer coefficients and number of generators equal to n. As such, ℜ( G) is a Unique Factorization Domain and thus, viewing a given representation of G as an element of this ring, it makes sense to ask questions about how a representation factors. Using various approaches we show that the types of factorizations which appear in the irreducible characters of G depend on the geometry of the root system and also have connections to the classifying space BG