Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: A geometric derivation of KdV-type hierarchies from root systems   For the root system of each complex semi-simple Lie algebra of rank two, and
for the associated 2D Toda chain $E=\{u_{xy}=\exp(K u)\}$, we calculate the two
first integrals of the characteristic equation $D_y(w)=0$ on $E$. Using the
integrals, we reconstruct and make coordinate-independent the $(2\times
2)$-matrix operators $\square$ in total derivatives that factor symmetries of
the chains. Writing other factorizations that involve the operators $\square$,
we obtain pairs of compatible Hamiltonian operators that produce KdV-type
hierarchies of symmetries for $\cE$. Having thus reduced the problem to the
Hamiltonian case, we calculate the Lie-type brackets, transferred from the
commutators of the symmetries in the images of the operators $\square$ onto
their domains. With all this, we describe the generators and derive all the
commutation relations in the symmetry algebras of the 2D Toda chains, which
serve here as an illustration for a much more general algebraic and geometric
set-up.

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The categories of this paper are: astro-ph
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The categories of this paper are: eess
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The categories of this paper are: cond-mat
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The categories of this paper are: gr-qc
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The categories of this paper are: acc-phys
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The categories of this paper are: hep-th
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The categories of this paper are: q-bio
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The categories of this paper are: math-ph
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The categories of this paper are: adap-org
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The categories of this paper are: physics
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The categories of this paper are: stat
29
The categories of this paper are: funct-an
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The categories of this paper are: supr-con
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The categories of this paper are: hep-lat
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The categories of this paper are: dg-ga
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The categories of this paper are: atom-ph