Mathematics Stack Exchange is a question and answer site for people studying math at any level and professionals in related fields. It's 100% free, no registration required.

Sign up
Here's how it works:
  1. Anybody can ask a question
  2. Anybody can answer
  3. The best answers are voted up and rise to the top

Here the ground field $k$ is algebriacally closed.$A$ is the algebra of upper triangular $n$ by $n$ matrices.

I already know that $V_i$ which is 1-dimensional, and any matrix $x$ acts by $x_{ii}$($x_{ii}$ is the ($i$,$i$)-th entry of $x$) is irreducible representation of $A$($i=1,2,...,n$).

I know a method to show that these are all the irreducible representations of $A$. It uses that fact that $A/Rad(A)=\bigoplus End(W_i)$ where $W_i$ are the pair-wise nonisomorphic irreducible representations of $A$.

Are there any other more direct method to do this?

Would someone be kind enough to give me some hints on this?Thank you very much!

share|cite|improve this question

Your Answer


By posting your answer, you agree to the privacy policy and terms of service.

Browse other questions tagged or ask your own question.