Langlands Dual Group

The Langlands dual group is a mathematical construction that relates symmetries of certain algebraic objects to those of other, often simpler, groups. In essence, it’s a way to pair complex structures (like groups arising from number theory or geometry) with "dual" groups that reflect their underlying symmetry in a different but connected form. This duality helps mathematicians understand deep relationships between different areas such as number theory and geometry, forming a key part of the Langlands program, which aims to unify various parts of mathematics through these symmetrical correspondences.