representation of Galois groups

Galois groups are mathematical structures that describe symmetries in solutions to polynomial equations. Representing these groups involves translating their abstract symmetries into concrete mathematical objects, like matrices or linear transformations, that act on vector spaces. This process makes it easier to analyze how the symmetries relate to the equations' properties. In essence, the representation provides a way to "visualize" and study the Galois group by presenting its complex symmetries through familiar, manageable mathematical tools, bridging the abstract concept with explicit algebraic structures.