Available at: https://digitalcommons.calpoly.edu/theses/3217
Date of Award
12-2025
Degree Name
MS in Mathematics
Department/Program
Mathematics
College
College of Science and Mathematics
Advisor
Robert Easton
Advisor Department
Mathematics
Advisor College
College of Science and Mathematics
Abstract
Classically, one of the central methods of understanding an abstract group has been through its representations in other structures, such as permutations of sets or linear transformations of vector spaces. As a detailed illustration of this method, we will focus on the matrix group SL(2,q), which consists of all invertible 2x2 matrices with entries in a finite field with q elements. We will outline the explicit construction of every (irreducible) complex representation of this group. Along the way we will also touch on foundational concepts in representation theory, such as characters and induced representations.