On the representation theory of GL(2,F_{q}).
| dc.contributor.author | Kaur, Gurjyot | |
| dc.contributor.examiningcommittee | Krepski, Derek (Mathematics) Zhang, Yang (Mathematics) | en_US |
| dc.contributor.supervisor | Chipalkatti, Jaydeep (Mathematics) Sankaran, Siddarth (Mathematics) | en_US |
| dc.date.accessioned | 2021-01-18T13:26:21Z | |
| dc.date.available | 2021-01-18T13:26:21Z | |
| dc.date.copyright | 2020-12-03 | |
| dc.date.issued | 2020-12-03 | en_US |
| dc.date.submitted | 2020-12-03T18:47:49Z | en_US |
| dc.degree.discipline | Mathematics | en_US |
| dc.degree.level | Master of Science (M.Sc.) | en_US |
| dc.description.abstract | Let $G=\GL(2, \mathbb{F}_q)$ denote the group of invertible $2\times 2$ matrices over the finite field $\mathbb{F}_q$, where $q$ is the power of a prime number. This thesis investigates the complex irreducible representations of $G$. Chapter 2 gives an overview of the general theory of finite-dimensional representations of a finite group over the complex numbers. In Chapter 3, we discuss the different types of conjugacy classes in $G$. It will turn out that there are four types, which altogether give $q^2-1$ conjugacy classes. By general theory, the number of irreducible representations distinguished up to isomorphism is also equal to $q^2-1$. These representations are explicitly constructed in Chapter 4. Some of them are derived from the permutation representation of $G$ on the projective line $\mathbb{P}^1(\FF_q)$, while the rest are induced from smaller subgroups of $G$. In the concluding chapter, we compute the irreducible decompositions of the tensor products of some of these irreducible representations by using the character table for irreducible $G$-representations. | en_US |
| dc.description.note | February 2021 | en_US |
| dc.identifier.uri | http://hdl.handle.net/1993/35256 | |
| dc.language.iso | eng | en_US |
| dc.rights | open access | en_US |
| dc.subject | Representation Theory (Abstract Algebra) Mathematics. | en_US |
| dc.title | On the representation theory of GL(2,F_{q}). | en_US |
| dc.type | master thesis | en_US |