Group action on finite set gives rise to a linear representation

Watch
Doctor_Wormhole
Badges: 13
Rep:
?
#1
Report Thread starter 1 week ago
#1
can someone explain this to me? I'm trying to prove this?
0
reply
zetamcfc
Badges: 19
Rep:
?
#2
Report 1 week ago
#2
(Original post by Doctor_Wormhole)
can someone explain this to me? I'm trying to prove this?
Firstly what are the definitions you are using, and what have you done so far?
0
reply
Doctor_Wormhole
Badges: 13
Rep:
?
#3
Report Thread starter 1 week ago
#3
this is what I'm doing. I reduced this action more intrisically as g(f)(x)=f(g^(-1)x) and defined group action and proved homomorphism
Attached files
Last edited by Doctor_Wormhole; 1 week ago
0
reply
zetamcfc
Badges: 19
Rep:
?
#4
Report 1 week ago
#4
(Original post by Doctor_Wormhole)
this is what I'm doing. I reduced this action more intrisically as g(f)(x)=f(g^(-1)x) and defined group action and proved homomorphism
Surely all you need to say is that you have a finite set X, so you can index the basis of a k vector space by X. Then your representation is just applying your group action to the index, i.e. \ \phi (g) \sum_{x \in \Omega} \lambda_{x} e_{x} = \sum_{x \in \Omega} \lambda_{x} e_{g . x} (Sorry if i've misunderstood the question.)
0
reply
Doctor_Wormhole
Badges: 13
Rep:
?
#5
Report Thread starter 1 week ago
#5
(Original post by zetamcfc)
Surely all you need to say is that you have a finite set X, so you can index the basis of a k vector space by X. Then your representation is just applying your group action to the index, i.e. \ \phi (g) \sum_{x \in \Omega} \lambda_{x} e_{x} = \sum_{x \in \Omega} \lambda_{x} e_{g . x} (Sorry if i've misunderstood the question.)
yeah that's what I understood too.
0
reply
X

Quick Reply

Attached files
Write a reply...
Reply
new posts
Back
to top
Latest
My Feed

See more of what you like on
The Student Room

You can personalise what you see on TSR. Tell us a little about yourself to get started.

Personalise

How are you feeling ahead of results day?

Very Confident (29)
8.43%
Confident (46)
13.37%
Indifferent (51)
14.83%
Unsure (83)
24.13%
Worried (135)
39.24%

Watched Threads

View All