Obtaining the immanent associated to a partition
For a partition λ let yλ be the corresponding irreducible representation of the symmetric group Sn. Let pλ=∑π∈Snyλ(π)x1π(1)...xnπ(n) be the immanent corresponding to λ. (For the sign representation we will just get the determinant for example). This is a polynomial in the n2 variables xi,j over Z.
My question is how can I obtain the immanent given a parition λ using Sage?
My first problem is already that we need the polynomial ring in the n2 variables xi,j and I am not sure how to define this in Sage depending on n.