Representations of Lie groups
So let's imagine we have some friends who like to play a game called "Lie Group." In this game, everyone has to stand in a certain way to make a shape. The rules are really strict, and each person has to follow them exactly or the shape won't work.
Now, each of our friends has one special way that they like to stand, and that way is called their "representation." It's like a special pose they have that helps them make the shape in the game.
But if we want to play this game with different people, we might need to use different poses. That's where "representations of Lie groups" come in. We can think of them like different sets of rules that people can follow to make the shape.
These different sets of rules are really important because they help us understand how the shape works in different ways. Some sets of rules might make the shape bigger or smaller, while others might twist it around in a different way.
So when we study representations of Lie groups, we're really studying how the different poses or rules affect the shape in the game. And that helps us understand how the game works and how to make it work better.
Now, each of our friends has one special way that they like to stand, and that way is called their "representation." It's like a special pose they have that helps them make the shape in the game.
But if we want to play this game with different people, we might need to use different poses. That's where "representations of Lie groups" come in. We can think of them like different sets of rules that people can follow to make the shape.
These different sets of rules are really important because they help us understand how the shape works in different ways. Some sets of rules might make the shape bigger or smaller, while others might twist it around in a different way.
So when we study representations of Lie groups, we're really studying how the different poses or rules affect the shape in the game. And that helps us understand how the game works and how to make it work better.