Fundamental representation
Imagine you have a bunch of toys that are all the same shape, but they have different colors. Now imagine you want to organize them in a special way, so you decide to group them all together based on their color. This is kind of like what mathematicians do when they talk about "representations".
In math, a "representation" is a fancy word that describes a way of organizing things based on a set of rules, or "symmetries". These rules might be things like "rotate 90 degrees" or "flip upside-down". Depending on what rules you choose, you can group things together in different ways.
Now, when we talk about a "fundamental representation", this just means that the rules we're using are the most basic ones possible. It's kind of like starting with the simplest set of building blocks, and using those to create more complex shapes.
For example, imagine we have some blocks that are all identical cubes. We might say that one "symmetry rule" we can use is to rotate the cube by 90 degrees. Using just this one rule, we can group together all the cubes that look the same after being rotated by 90, 180, or 270 degrees. This is an example of a fundamental representation.
So in summary, a fundamental representation is just a simple way of organizing things (like blocks or equations) based on a set of basic rules (or "symmetries"). It's kind of like starting with a basic building block and using that as a foundation for more complex structures.
In math, a "representation" is a fancy word that describes a way of organizing things based on a set of rules, or "symmetries". These rules might be things like "rotate 90 degrees" or "flip upside-down". Depending on what rules you choose, you can group things together in different ways.
Now, when we talk about a "fundamental representation", this just means that the rules we're using are the most basic ones possible. It's kind of like starting with the simplest set of building blocks, and using those to create more complex shapes.
For example, imagine we have some blocks that are all identical cubes. We might say that one "symmetry rule" we can use is to rotate the cube by 90 degrees. Using just this one rule, we can group together all the cubes that look the same after being rotated by 90, 180, or 270 degrees. This is an example of a fundamental representation.
So in summary, a fundamental representation is just a simple way of organizing things (like blocks or equations) based on a set of basic rules (or "symmetries"). It's kind of like starting with a basic building block and using that as a foundation for more complex structures.