Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Toda lattice, cohomology of compact Lie groups and finite Chevalley
  groups   In this paper, we describe a connection that exists among (a) the number of
singular points along the trajectory of Toda flow, (b) the cohomology of a
compact subgroup $K$, and (c) the number of points of a Chevalley group
$K({\mathbb F}_q)$ related to $K$ over a finite field ${\mathbb F}_q$. The Toda
lattice is defined for a real split semisimple Lie algebra $\mathfrak g$, and
$K$ is a maximal compact Lie subgroup of $G$ associated to $\mathfrak g$.
Relations are also obtained between the singularities of the Toda flow and the
integral cohomology of the real flag manifold $G/B$ with $B$ the Borel subgroup
of $G$ (here we have $G/B=K/T$ with a finite group $T$). We also compute the
maximal number of singularities of the Toda flow for any real split semisimple
algebra, and find that this number gives the multiplicity of the singularity at
the intersection of the varieties defined by the zero set of Schur polynomials.

1
The categories of this paper are: cs
13
The categories of this paper are: quant-ph
3
The categories of this paper are: physics
32
The categories of this paper are: atom-ph
6
The categories of this paper are: astro-ph
19
The categories of this paper are: eess
22
The categories of this paper are: chao-dyn
33
The categories of this paper are: plasm-ph
10
The categories of this paper are: q-bio
12
The categories of this paper are: nucl-th
26
The categories of this paper are: bayes-an
29
The categories of this paper are: funct-an
24
The categories of this paper are: dg-ga
14
The categories of this paper are: math-ph
7
The categories of this paper are: hep-th
35
The categories of this paper are: mtrl-th