Representation theory quick question
Answer
Answers can only be viewed under the following conditions:
- The questioner was satisfied with and accepted the answer, or
- The answer was evaluated as being 100% correct by the judge.
-
Thank you! Is there any way to show that these are indeed the only subrepresentations?
-
Yes. The one-dimensional subrep is clearly irreducible and the 2-dim is as well, since rho(x) and rho(y) do not have any common eigenspace. So any other subrep must decompose as a sum of irred. reps, which must be the ones previously found. But the only options then are U, V, and U+V = F_2^3.
-
*any other common eigenspace
-
Hello there, are you available to answer some more questions today, with a $60 price for each? They're related to fields and Galois theory
The answer is accepted.
Join Matchmaticians Affiliate Marketing
Program to earn up to a 50% commission on every question that your affiliated users ask or answer.
- answered
- 1082 views
- $20.00
Related Questions
- Compounding interest of principal P, where a compounding withdrawal amount W get withdrawn from P before each compounding of P.
- How do you go about solving this question?
- Induced and restricted representation
- Find the null space of the matrix $\begin{pmatrix} 1 & 2 & -1 \\ 3 & -3 & 1 \end{pmatrix}$
- Help needed finding a formula
- Center of algebra of functions
- Find $x$, if $\sqrt{x} + 2y^2 = 15$ and $\sqrt{4x} − 4y^2 = 6$.
- Algebra Word Problem 3