Physics – High Energy Physics – High Energy Physics - Theory
Scientific paper
1992-10-08
Commun.Math.Phys. 154 (1993) 181-214
Physics
High Energy Physics
High Energy Physics - Theory
43 pages
Scientific paper
10.1007/BF02096838
Generalized Drinfeld-Sokolov (DS) hierarchies are constructed through local reductions of Hamiltonian flows generated by monodromy invariants on the dual of a loop algebra. Following earlier work of De Groot et al, reductions based upon graded regular elements of arbitrary Heisenberg subalgebras are considered. We show that, in the case of the nontwisted loop algebra $\ell(gl_n)$, graded regular elements exist only in those Heisenberg subalgebras which correspond either to the partitions of $n$ into the sum of equal numbers $n=pr$ or to equal numbers plus one $n=pr+1$. We prove that the reduction belonging to the grade $1$ regular elements in the case $n=pr$ yields the $p\times p$ matrix version of the Gelfand-Dickey $r$-KdV hierarchy, generalizing the scalar case $p=1$ considered by DS. The methods of DS are utilized throughout the analysis, but formulating the reduction entirely within the Hamiltonian framework provided by the classical r-matrix approach leads to some simplifications even for $p=1$.
Feher Laszlo
Harnad John
Marshall Ian
No associations
LandOfFree
Generalized Drinfeld-Sokolov Reductions and KdV Type Hierarchies does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.
If you have personal experience with Generalized Drinfeld-Sokolov Reductions and KdV Type Hierarchies, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Generalized Drinfeld-Sokolov Reductions and KdV Type Hierarchies will most certainly appreciate the feedback.
Profile ID: LFWR-SCP-O-166031