Discrete series representation

Imagine you have little toys that represent different things, like animals and vehicles. Each toy belongs to a certain group, like all the cars belong to the "car group" and all the dogs belong to the "dog group". We can also group these toys by size; some toys are big and some are small.

In math, we can group things too, but instead of toys we have numbers. We can group numbers by adding them up. For example, we can group 3 and 4 to get 7. We can also group numbers by how they behave when we do math with them. This is called a "representation".

Discrete series representation is a way of grouping numbers that helps us solve math problems. We group numbers by how they transform or change when we do certain math operations with them. Just like our toy cars all have wheels and our toy dogs all have tails, these numbers all behave in the same way when we do math with them.

Using discrete series representation, we can simplify complicated math problems into simpler ones that are easier to solve. It's like taking a big pile of toys and sorting them into groups so we know where to find what we need.