Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Lowest degree invariant 2nd order PDEs over rational homogeneous contact
  manifolds   For each simple Lie algebra $\mathfrak{g}$ (excluding, for trivial reasons,
type ${\sf C}$) we find the lowest possible degree of an invariant second-order
PDE over the adjoint variety in $\mathbb{P}\mathfrak{g}$, a homogeneous contact
manifold. Here a PDE $F(x^i,u,u_i,u_{ij})=0$ has degree $\le d$ if $F$ is a
polynomial of degree $\le d$ in the minors of $(u_{ij})$, with coefficients
functions of the contact coordinates $x^i$, $u$, $u_i$ (e.g., Monge-Amp\`ere
equations have degree 1). For $\mathfrak{g}$ of type ${\sf A}$ or ${\sf G}$ we
show that this gives all invariant second-order PDEs. For $\mathfrak{g}$ of
type ${\sf B}$ and ${\sf D}$ we provide an explicit formula for the
lowest-degree invariant second-order PDEs. For $\mathfrak{g}$ of type ${\sf E}$
and ${\sf F}$ we prove uniqueness of the lowest-degree invariant second-order
PDE; we also conjecture that uniqueness holds in type ${\sf D}$.

25
The categories of this paper are: patt-sol
0
The categories of this paper are: hep-ph
30
The categories of this paper are: q-alg
12
The categories of this paper are: nucl-th
10
The categories of this paper are: q-bio
29
The categories of this paper are: funct-an
3
The categories of this paper are: physics
13
The categories of this paper are: quant-ph
6
The categories of this paper are: astro-ph
35
The categories of this paper are: mtrl-th
15
The categories of this paper are: nucl-ex
36
The categories of this paper are: cmp-lg
17
The categories of this paper are: q-fin
31
The categories of this paper are: ao-sci
4
The categories of this paper are: cond-mat
22
The categories of this paper are: chao-dyn