# Questions tagged [schur-functions]

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### How to re-expand the sum of Schur function?

Consider next sum \begin{eqnarray} \label{PF_spindef} Z = \sum_{r=0}^{N N_f} h^{2r} \ Q(r) . \end{eqnarray} and \begin{equation} Q(r) \ = \ \sum_{\sigma \vdash r} s_{\sigma}(1^{N_f}) \ s_{\sigma}...
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### proof of result from Ian Macdonald's paper "A New Class of Symmetric Functions"

I'm currently working my way through Ian MacDonald's somewhat seminal 1988 paper entitled "A New Class of Symmetric Functions" in Seminaire Lotharingien B20a, pp. 131–171 (EuDML). I'm fine ...
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### Double Schur function expansion

In literature, I have seen the weighted Hurwitz number $N_{g,n}(d_1 , d_2 \ldots , d_n)$ which are symmetric number and they can be written as double Schur function expansion. \begin{align} \label{eq:...
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### what is the link between plethysm in regular representation of the symmetric group and plethysm in Schur functions.

I am trying to understand first how one can define the plethysm say $s_\lambda \circ s_\mu$ as a module in the regular representation of the symmetric group. 1)How is it connected to the plethysms ...
I am writing a paper(physics) where I am using the fact that the irreducible's of the regular representations of the permutation group are absolutely irreducible in the following sense. If $V$ is an ...
Recall the Schur polynomial in $n$ variables, indexed by the partition $\lambda$, with $\ell(\lambda) \leq n$, is given by \begin{equation} s_\lambda(x_1,\ldots, x_n) = a_{\lambda + \delta}(x_1, \...