Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Symmetric polynomials in the symplectic alphabet and their expression
  via Dickson--Zhukovsky variables   Given a symmetric polynomial $P$ in $2n$ variables, there exists a unique
symmetric polynomial $Q$ in $n$ variables such that \[
P(x_1,\ldots,x_n,x_1^{-1},\ldots,x_n^{-1})
=Q(x_1+x_1^{-1},\ldots,x_n+x_n^{-1}). \] We denote this polynomial $Q$ by
$\Phi_n(P)$ and show that $\Phi_n$ is an epimorphism of algebras. We compute
$\Phi_n(P)$ for several families of symmetric polynomials $P$: symplectic and
orthogonal Schur polynomials, elementary symmetric polynomials, complete
homogeneous polynomials, and power sums. Some of these formulas were already
found by Elouafi (2014) and Lachaud (2016).
  The polynomials of the form $\Phi_n(\operatorname{s}_{\lambda/\mu}^{(2n)})$,
where $\operatorname{s}_{\lambda/\mu}^{(2n)}$ is a skew Schur polynomial in
$2n$ variables, arise naturally in the study of the minors of symmetric banded
Toeplitz matrices, when the generating symbol is a palindromic Laurent
polynomial, and its roots can be written as
$x_1,\ldots,x_n,x^{-1}_1,\ldots,x^{-1}_n$. Trench (1987) and Elouafi (2014)
found efficient formulas for the determinants of symmetric banded Toeplitz
matrices. We show that these formulas are equivalent to the result of Ciucu and
Krattenthaler (2009) about the factorization of the characters of classical
groups.

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The categories of this paper are: adap-org
23
The categories of this paper are: solv-int
4
The categories of this paper are: cond-mat
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The categories of this paper are: quant-ph
8
The categories of this paper are: hep-ex
3
The categories of this paper are: physics
17
The categories of this paper are: q-fin
31
The categories of this paper are: ao-sci
22
The categories of this paper are: chao-dyn
27
The categories of this paper are: comp-gas
1
The categories of this paper are: cs
34
The categories of this paper are: chem-ph
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The categories of this paper are: econ
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The categories of this paper are: gr-qc
0
The categories of this paper are: hep-ph
33
The categories of this paper are: plasm-ph