The Irreducible Representations of D2n

<p>Irreducible representations of a finite group over a field are important because all representations of a group are direct sums of irreducible representations. Maschke tells us that if φ is a representation of the finite group G of order n on the m-dimensional space V over the field K of complex numbers and if U is an invariant subspace of φ, then U has a complementary reducing subspace W .</p> <p>The objective of this thesis is to find all irreducible representations of the dihedral group D2n. The reason we will work with the dihedral group is because it is one of the first and most intuitive non-abelian group we encounter in abstract algebra. I will compute the representations and characters of D2n and my thesis will be an explanation of these computations. When n = 2k + 1 we will show that there are k + 2 irreducible representations of D2n, but when n = 2k we will see that D2n has k + 3 irreducible rep- resentations. To achieve this we will first give some background in group, ring, module, and vector space theory that is used in representation theory. We will then explain what general representation theory is. Finally we will show how we arrived at our conclusion.</p>

Name thesis:degree_name

Master of Arts in Mathematics

Level thesis:degree_level

Thesis

Discipline thesis:degree_discipline

Mathematics

Year dc:date.available

2014

Author dc:creator

• Soto, Melissa

Contributors dc:contributor

• Dr. Giovanna Llosent

• Representation Theory
• Irreducible Representations
• Dihedral Group
• Algebra

Repository record dc:identifier

https://scholarworks.lib.csusb.edu/etd/12

OAI identifier oai:identifier

oai:scholarworks.lib.csusb.edu:etd-1005