Date of Award
Spring 2010
Degree Type
Dissertation
Degree Name
Doctor of Philosophy (PhD)
Graduate Group
Mathematics
First Advisor
Alexandre Kirillov
Abstract
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 tensor product, direct sum, and direct difference 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.
Recommended Citation
Rupinski, Andrew, "Factorizations in the Irreducible Characters of Compact Semisimple Lie Groups" (2010). Publicly Accessible Penn Dissertations. 140.
https://repository.upenn.edu/edissertations/140