TY - JOUR
T1 - Classical W-algebras and generalized Drinfeld-Sokolov hierarchies for minimal and short nilpotents
JF - Communications in Mathematical Physics 331, nr. 2 (2014) 623-676
Y1 - 2014
A1 - Alberto De Sole
A1 - Victor G. Kac
A1 - Daniele Valeri
AB - We derive explicit formulas for lambda-brackets of the affine classical W-algebras attached to the minimal and short nilpotent elements of any simple Lie algebra g. This is used to compute explicitly the first non-trivial PDE of the corresponding intgerable generalized Drinfeld-Sokolov hierarchies. It turns out that a reduction of the equation corresponding to a short nilpotent is Svinolupov's equation attached to a simple Jordan algebra, while a reduction of the equation corresponding to a minimal nilpotent is an integrable Hamiltonian equation on 2h-3 functions, where h is the dual Coxeter number of g. In the case when g is sl_2 both these equations coincide with the KdV equation. In the case when g is not of type C_n, we associate to the minimal nilpotent element of g yet another generalized Drinfeld-Sokolov hierarchy.
PB - SISSA
UR - http://hdl.handle.net/1963/6979
N1 - 46 pages
U1 - 6967
U2 - Mathematics
U4 - 1
U5 - MAT/07 FISICA MATEMATICA
ER -