TY - JOUR AU - Aburto-Hageman, Luisa AU - Johnson, Roberto AU - Pantoja, José PY - 2017/05/08 Y2 - 2024/03/29 TI - The complex linear representations of GL(2, k), k a finite field JF - Proyecciones (Antofagasta, On line) JA - Proyecciones (Antofagasta, On line) VL - 25 IS - 3 SE - DO - 10.4067/S0716-09172006000300007 UR - https://www.revistaproyecciones.cl/index.php/proyecciones/article/view/1539 SP - 307-329 AB - <span class="fontstyle0">Let </span><span class="fontstyle2">k </span><span class="fontstyle0">be a finite field of odd characteristic, and let </span><span class="fontstyle2">G </span><span class="fontstyle0">be the group of all invertible </span><span class="fontstyle3">2 </span><span class="fontstyle4">× </span><span class="fontstyle3">2 </span><span class="fontstyle0">matrices over </span><span class="fontstyle2">k. </span><span class="fontstyle0">We construct the irreducible complex linear representations of the group </span><span class="fontstyle2">G.</span><span class="fontstyle0">The constructions lean on the method of induction from subgroups and on the theory of characters. To accomplish this goal, the basic facts from the theory of representations and characters of finite groups are presented. Furthermore, we describe the structure of </span><span class="fontstyle2">G </span><span class="fontstyle0">that we need, and the theory of representations of some subgroups of </span><span class="fontstyle2">G </span><span class="fontstyle0">that we use. As a final result, we obtain the theory of the irreducible representations of </span><span class="fontstyle2">G,</span><span class="fontstyle0">by describing either the irreducible representations of , or the irreducible characters of the group </span><span class="fontstyle2">G.</span> ER -