Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Semi-invariants and Integrals of the Full Symmetric sl(n) Toda Lattice   We consider the full symmetric version of the Lax operator of the Toda
lattice which is known as the full symmetric Toda lattice. The phase space of
this system is the generic orbit of the coadjoint action of the Borel subgroup
B^+(n) of SL(n,R). This system is integrable. We propose a new method of
constructing semi-invariants and integrals of the full symmetric Toda lattice.
Using only the Toda equations for the Lax eigenvector matrix we prove the
existence of the semi-invariants which are Plucker coordinates in the
corresponding projective spaces. Then we use these semi-invariants to construct
the integrals. It is known that the full symmetric sl(n) Toda lattice has
additional integrals which can be produced by Kostant procedure except for the
integrals which can be derived by the chopping procedure. Altogether these
integrals constitute a full set of the independent non-involutive integrals.
Yet the unsolved complicated technical problem is their explicit derivation
since Kostant procedure has crucial computational complexities even for
low-rank Lax matrices and is practically unapplicable for higher ranks. Our new
approach provides a resolution of this problem and results in simple explicit
formulae for the full set of independent semi-invariants and integrals
expressed both in terms of the Lax matrix and its eigenvector and eigenvalue
matrices of the full symmetric sl(n) Toda lattice without using the chopping
and Kostant procedures. We also describe the structure of the additional
integrals of motion as functions on the flag space modulo the Toda flows and
show how Plucker coordinates of different projective spaces define different
families of the additional integrals. In this paper we present detailed proofs
of the propositions of [24].

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The categories of this paper are: cmp-lg
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The categories of this paper are: physics
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The categories of this paper are: nucl-th
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The categories of this paper are: eess
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The categories of this paper are: hep-lat
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The categories of this paper are: q-bio
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The categories of this paper are: chem-ph
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The categories of this paper are: hep-ex
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The categories of this paper are: mtrl-th
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The categories of this paper are: acc-phys
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The categories of this paper are: plasm-ph
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The categories of this paper are: hep-ph
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The categories of this paper are: supr-con
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The categories of this paper are: comp-gas
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The categories of this paper are: cond-mat
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The categories of this paper are: funct-an