Factorizations in the irreducible characters of compact semisimple lie groups / Andrew Rupinski.

Format:

Book

Manuscript

Thesis/Dissertation

Author/Creator:

Rupinski, Andrew.

Contributor:

Kirillov, Alexandre, advisor.

University of Pennsylvania.

Language:

English

Subjects (All):

Penn dissertations--Mathematics.

Mathematics--Penn dissertations.

Local Subjects:

Penn dissertations--Mathematics.

Mathematics--Penn dissertations.

Physical Description:

v, 119 pages ; 29 cm

Production:

2010.

Summary:

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 reals(G) with the operations of ⊗, ⊕, and ⊖ , is isomorphic to a polynomial ring with integer coefficients and number of generators equal to n. As such, reals( 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.

Notes:

Adviser: Alexandre Kirillov.

Thesis (Ph.D. in Mathematics) -- University of Pennsylvania, 2010.

Includes bibliographical references.