Factorizations in the irreducible characters of compact semisimple Lie groups.

Format:

• Book
• Thesis/Dissertation

Author/Creator:

• Rupinski, Andrew.

Contributor:

• Kirillov, Alexandre, advisor.
• University of Pennsylvania.

Language:

English

Subjects (All):

• Mathematics.
• 0405.
• 0642.
• Penn dissertations--Mathematics.
• Mathematics--Penn dissertations.

Local Subjects:

• Penn dissertations--Mathematics.
• Mathematics--Penn dissertations.
• 0405.
• 0642.

Physical Description:

125 pages

Contained In:

Dissertation Abstracts International 71-12B.

System Details:

• Mode of access: World Wide Web.
• text file

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:

• Thesis (Ph.D. in Mathematics) -- University of Pennsylvania, 2010.
• Source: Dissertation Abstracts International, Volume: 71-12, Section: B, page: 7466.
• Adviser: Alexandre Kirillov.

Local Notes:

School code: 0175.

ISBN:

9781124318202

Access Restriction:

Restricted for use by site license.