Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: The full Kostant-Toda hierarchy on the positive flag variety   We study some geometric and combinatorial aspects of the solution to the full
Kostant-Toda (f-KT) hierarchy, when the initial data is given by an arbitrary
point on the totally non-negative (tnn) flag variety of SL_n(R). The f-KT flows
on the tnn flag variety are complete, and their asymptotics are completely
determined by the cell decomposition of the tnn flag variety given by Rietsch.
We define the f-KT flow on the weight space via the moment map, and show that
the closure of each f-KT flow forms an interesting convex polytope generalizing
the permutohedron which we call a Bruhat interval polytope. We also prove
analogous results for the full symmetric Toda hierarchy, by mapping our f-KT
solutions to those of the full symmetric Toda hierarchy. In the Appendix we
show that Bruhat interval polytopes are generalized permutohedra, in the sense
of Postnikov, and that their edges correspond to cover relations in the Bruhat
order.

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The categories of this paper are: funct-an
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The categories of this paper are: comp-gas
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The categories of this paper are: q-fin
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The categories of this paper are: astro-ph
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The categories of this paper are: mtrl-th
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The categories of this paper are: nucl-th
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The categories of this paper are: hep-ph
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The categories of this paper are: dg-ga
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The categories of this paper are: patt-sol
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The categories of this paper are: hep-lat
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The categories of this paper are: hep-ex
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The categories of this paper are: alg-geom
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The categories of this paper are: chem-ph
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The categories of this paper are: eess
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The categories of this paper are: adap-org
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The categories of this paper are: physics