Weyl group

A Weyl group is like a club made up of special friends who like to play with shapes, called "symmetries." They have rules for how to move these shapes around in certain ways, kind of like a game.

Each friend in the club has a special strategy that they use to make sure the game goes smoothly. They are like different "players" in the game that work together to make sure everyone wins.

When they move the shapes around, they are careful not to change the way they look too much. They like to keep things nice and symmetrical, and they have to use special moves to make sure nothing gets messed up.

Sometimes, if they need to add a new shape to the mix, they have to change the rules a little bit. It's like they're making a new game that they can all play together.

But even with all of these special moves and rules, the Weyl group still manages to make everything look pretty and organized. And through their games, they help us understand more about how shapes and symmetries work together.