3

What is the intuition behind verma modules? Their construction is quite technical to me and I know they help classify irreducible representations and are very useful, but I cannot see how. In class, we didn´t explicitly use them for anything, so I am confused.

What are the verma modules intuitively? How would you interpret the construction in easier words so one can try to sketch them or imagine their relation to other concepts?

I am using the definition/construction of Verma modules below, also seen the constructions on Wikipedia.

enter image description here

Tereza Tizkova
  • 2,750

1 Answers1

5

I don't know whether you would view this as an "intuitive" description, but a Verma module is the largest possible module of a semisimple Lie algebra that is generated by a single highest weight vector. This means that any module generated by a single highest weight vector of the same weight has to be a quotient of the Verma module. So it is kind of a "universal object" which is characterized by its properties.

Andreas Cap
  • 22,380