Lowest degree invariant second-order PDEs over rational homogeneous contact manifolds

Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F62690094%3A18470%2F19%3A50017605" target="_blank" >RIV/62690094:18470/19:50017605 - isvavai.cz</a>
Result on the web
<a href="https://www.worldscientific.com/doi/abs/10.1142/S0219199717500894" target="_blank" >https://www.worldscientific.com/doi/abs/10.1142/S0219199717500894</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.1142/S0219199717500894" target="_blank" >10.1142/S0219199717500894</a>

Result language
angličtina
Original language name
Lowest degree invariant second-order PDEs over rational homogeneous contact manifolds
Original language description
For each simple Lie algebra g (excluding, for trivial reasons, type C), we find the lowest possible degree of an invariant second-order PDE over the adjoint variety in Pg, a homogeneous contact manifold. Here a PDE F (x(i), u, u(i),( )u(ij)) = 0 has degree <= d if F is a polynomial of degree <= d in the minors of (u(ij)), with coefficient functions of the contact coordinate x(i), u, u(i) (e.g., Monge-Ampbre equations have degree 1). For g of type A or G(2), we show that this gives all invariant second-order PDEs. For g of types B and D, we provide an explicit formula for the lowest-degree invariant second-order PDEs. For g of types E and F-4, we prove uniqueness of the lowest-degree invariant second-order PDE; we also conjecture that uniqueness holds in type D.
Czech name
—
Czech description
—

Type
J<sub>imp</sub> - Article in a specialist periodical, which is included in the Web of Science database
CEP classification
—
OECD FORD branch
10101 - Pure mathematics

Project
—
Continuities
I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace

Publication year
2019
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

Similar results(10)