1
vote
0answers
22 views

Dimension of the Image of Young Projectors corresponding to Tensor factors.

Suppose I define the action of the symmetric group on abstract tensors as shuffling indices. I know this is very naive. I apologise, I am a physicist and working on a problem that involves tensors ...
9
votes
1answer
149 views

Generalizing Newton's identities: Trace formula for Schur functors

We work over $\mathbb C$. A general linear group ${\rm GL}(V)$ acts diagonally on the tensor power $V^{\otimes n}$ as $$(A^{\otimes n})(v_1\otimes\cdots\otimes v_n):=(Av_1)\otimes\cdots\otimes ...
0
votes
0answers
26 views

Identity with symmetric rational functions

I am trying to prove this identity between rational functions involving symmetrization among variables. Let us consider a set of variables $\{p_1,\ldots,p_n\}$, which I indicate globally as ...
0
votes
0answers
72 views

Is there a subgroup of $S_{10}$ having $5040$ elements other than $S_7$?

I'm trying to generate to monomial symmetric polynomial $$ m_{(1,2,3,4)}(X_1,X_2,\dots,X_{10})=X_1^1X_2^2X_3^3X_4^4 + \text{all permutations,} $$ starting from the first element by applying all ...
4
votes
0answers
73 views

Die Relationen, welche zwischen den elementaren symmetrischen Functionen bestehen - Translation?

I am trying to find a translation of this paper either in English or French (preferably English). I am not very optimistic, but i thought of asking in case somebody is more resourceful :)
1
vote
0answers
72 views

Symmetrization of Powersum polynomials

Let $n\in\mathbb{N}$. Then for $i\in\mathbb{N}$ the $i-$th power sum if defined to be $p_i^{(n)}:=\sum_{j=1}^n x_j^i$. Then let $\lambda:=(\lambda_1,\ldots,\lambda_l)$ be a partition of $d$. We can ...
2
votes
1answer
154 views

Identifying $k[x_1,x_2,y_1,y_2]^{\epsilon}$ with $k[x,y]\wedge k[x,y]$

Suppose the symmetric group $S_2$ of order 2 acts on $k^4=Spec \;k[x_1, x_2, y_1, y_2]$ by the following: for $\sigma\not=e$, $$\sigma\circ(x_1, x_2, y_1, y_2)=(x_2,x_1,y_2,y_1).$$ That is, the ...