I am going through "Linear group representations" by Ernest Vinberg
The example is given below:
But I have difficulties in understanding the following:
1- why $V_{0}$ is called $(n-1)-$dimensional subspace, I want a concrete example please?
2- Why if the characteristic of the field $K$ is equal to zero, then $V_{1}$ is not subset of $V_{0}$?
3- I do not understand how he calculated $M((12))x – x$, could anyone clarify this for me?
4- Now I am stuck on this question (the above example is example 5):
Best Answer
I can answer to the first three questions: