A highest weight module is a type of module over a Lie algebra, particularly in the context of representation theory, characterized by a highest weight vector that generates the entire module. This vector is annihilated by all positive root vectors and corresponds to the highest weight in a specified weight space, reflecting the module's structure. Highest weight modules are essential in understanding the representation theory of quantum groups and their links to quantum enveloping algebras.
congrats on reading the definition of highest weight module. now let's actually learn it.