automorphic representations
Automorphic representations are mathematical objects in the field of number theory and representation theory. They generalize the concept of modular forms and are associated with Lie groups and algebraic groups. These representations help in understanding the symmetries and structures of various mathematical entities, particularly in relation to automorphic forms.
In essence, automorphic representations provide a framework for studying how certain functions behave under transformations of a group. They play a crucial role in connecting different areas of mathematics, such as number theory, geometry, and harmonic analysis, and are instrumental in proving significant results, including the Langlands program.