Schur functor

Okay, so imagine you have a big box filled with smaller boxes. Each smaller box has some toys inside that your friends have given you as presents. You want to group these toys together in a special way. One way is to put all the toys of the same color in one box. Another way is to put all the toys of the same shape in one box.

Now imagine that instead of toys, you have mathematical objects called vectors. These vectors have numbers inside them that tell you how big and in which direction they are. Just like you grouped toys together, mathematicians want to group vectors together in a special way.

That's where the Schur functor comes in. It's like a big toolbox that lets you group vectors together based on their qualities. For example, you could group vectors together based on their symmetries or the way they transform under certain operations.

To do this, the Schur functor takes in a bunch of vectors and puts them into new boxes based on their shared qualities. This process is called taking a Schur functor. It's like a magic trick where you can turn one big box of vectors into many smaller boxes of vectors that are grouped in a special way.

So when someone talks about the Schur functor, they're really talking about a tool that lets you group mathematical objects together in a special way. Just like you grouped toys together based on their qualities, mathematicians use the Schur functor to group vectors together based on their shared qualities.