Homework question regarding irreducible representations

In summary, the conversation discusses the process of finding irreducible representations for the C2, C3, and C3v groups. The speaker is struggling to find the irreducible representation for the C2 group and is also unsure about the order of finding the matrix M and the irreducible representation. The conversation also touches on the possibility of using different fields for the representations.
  • #1
PhysKid24
22
0
Hi,

I keep having problems with a homework question regarding irreducible representations. For the C2 group,which has only two elements,say, e and a, Iwas able to find the regular representations for them, yet i don't know how to find an irreducible representation for them. I'm also supposed to find a matrix M which diagonalizes D(reg)? Do I find M first and then the irreducible representation?Can anyone help?? I'm also to do the same procedure for group C3 and C3v. Thanks.
 
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  • #2
PhysKid24 said:
Hi,

I keep having problems with a homework question regarding irreducible representations. For the C2 group,which has only two elements,say, e and a, Iwas able to find the regular representations for them, yet i don't know how to find an irreducible representation for them. I'm also supposed to find a matrix M which diagonalizes D(reg)? Do I find M first and then the irreducible representation?
Find M first. The eigenspaces will be the irreducible reps
 
  • #3
Presuming you mean over R ro C or even Q.
what about the map sending a to 1, and the map sending a to -1 in any of these spaces?
 
  • #4
matt grime said:
Presuming you mean over R ro C or even Q.
I think any field of characteristic other than 2 will work.
 
  • #5
it even works with char 2. there is one simple rep in char 2, this gives it twice.
 

What is an irreducible representation?

An irreducible representation is a type of mathematical representation used to describe the symmetries of a physical system. It is a simplified version of a larger representation, where no further simplification can be made.

Why are irreducible representations important?

Irreducible representations are important because they allow us to analyze the symmetries of a system in a more manageable way. They also help us understand the physical properties and behavior of a system.

How are irreducible representations used in chemistry?

In chemistry, irreducible representations are used to classify molecular vibrations and electronic transitions. They also play a crucial role in determining the electronic structure of molecules and predicting their spectroscopic properties.

What is the difference between reducible and irreducible representations?

A reducible representation can be broken down into smaller representations, while an irreducible representation cannot be further simplified. In other words, an irreducible representation is the simplest form of a larger representation.

How are irreducible representations determined?

Irreducible representations can be determined by using character tables, which are organized tables that contain information about the symmetry elements and operations of a system. By applying these operations to basis functions, we can determine the symmetry properties of a system and classify them into irreducible representations.

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