3
votes
2answers
297 views

degrees of the invariants for the action of $SL(V)$ on $\wedge^4V$

How can we find the degrees of the invariants for the action of $SL(V)$ on $\wedge^4V$ , $dimV=8$ by the model in the Lie algebra $E_7$.
2
votes
1answer
189 views

When the affine quotient is faithfully flat?

It may be easy for the expert. Consider the map from $n$ by $m$ matrices (over $\mathbb{C}$ )to the $n$ by $n$ symmetric matrices $\phi\colon A\mapsto A A^T$. My question is when this map is ...
10
votes
1answer
492 views

When Are Quotients Complete Intersections?

Let $S_{n}$ denote the permutation group on $n$ letters and $G\subset S_{n}$ a transitive subgroup. The inclusion of $G$ in $S_{n}$ defines an action of $G$ on $\mathbb{C}^{n}$. By finding a ...