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7 papers · 1 filter
On the integrability conditions for some structures related to evolution differential equations
Paul Kersten, Iosif Krasil'shchik, Alexander Verbovetsky
Using the result by D.Gessler (Differential Geom. Appl. 7 (1997) 303-324, DIPS-9/98, http://diffiety.ac.ru/preprint/98/09_98abs.htm), we show that any invariant variational bivecto…
Regions in the dominant chamber and nilpotent orbits
Dmitri I. Panyushev
We give a geometric description for the dominant characteristic of a nilpotent orbit in an arbitrary finite-dimensional rational G-module. In particular, we obtain a generalization…
(Non)local Hamiltonian and symplectic structures, recursions, and hierarchies: a new approach and applications to the N=1 supersymmetric KdV equation
Paul Kersten, Iosif Krasil'shchik, Alexander Verbovetsky
Using methods of math.DG/0304245 and [I.S.Krasil'shchik and P.H.M.Kersten, Symmetries and recursion operators for classical and supersymmetric differential equations, Kluwer, 2000]…
Schubert varieties and the fusion products
B. Feigin, E. Feigin
For each we define a Schubert variety as a closure of the $\Slt(\C[t])$-orbit in the projectivization of the fusion product . We clarify the connection of t…
Short antichains in root systems, semi-Catalan arrangements, and B-stable subspaces
Dmitri I. Panyushev
Let $\be$ be a Borel subalgebra of a complex simple Lie algebra $\g$. An ideal of $\be$ is called ad-nilpotent, if it is contained in $[\be,\be]$. The generators of an ad-nilpotent…
Long Abelian ideals
Dmitri I. Panyushev
We study Abelian ideals of a Borel subalgebra consisting of long roots. It is shown that methods of Cellini and Papi can be extended to this situation. A uniform expression for the…