Physics – High Energy Physics – High Energy Physics - Theory
Scientific paper
1994-09-03
Annals Phys. 243 (1995) 372-419
Physics
High Energy Physics
High Energy Physics - Theory
Improved version with more specific results concerning the class of W-algebras which are defined in terms of soliton equations
Scientific paper
10.1006/aphy.1995.1102
We derive sufficient conditions under which the ``second'' Hamiltonian structure of a class of generalized KdV-hierarchies defines one of the classical $\cal W$-algebras obtained through Drinfel'd-Sokolov Hamiltonian reduction. These integrable hierarchies are associated to the Heisenberg subalgebras of an untwisted affine Kac-Moody algebra. When the principal Heisenberg subalgebra is chosen, the well known connection between the Hamiltonian structure of the generalized Drinfel'd-Sokolov hierarchies - the Gel'fand-Dickey algebras - and the $\cal W$-algebras associated to the Casimir invariants of a Lie algebra is recovered. After carefully discussing the relations between the embeddings of $A_1=sl(2,{\Bbb C})$ into a simple Lie algebra $g$ and the elements of the Heisenberg subalgebras of $g^{(1)}$, we identify the class of $\cal W$-algebras that can be defined in this way. For $A_n$, this class only includes those associated to the embeddings labelled by partitions of the form $n+1= k(m) + q(1)$ and $n+1= k(m+1) + k(m) + q(1)$.
Fernandez-Pousa Carlos R.
Gallas M. V.
Guillen Joaquin Sanchez
Miramontes Luis J.
No associations
LandOfFree
W-Algebras from Soliton Equations and Heisenberg Subalgebras 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 W-Algebras from Soliton Equations and Heisenberg Subalgebras, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and W-Algebras from Soliton Equations and Heisenberg Subalgebras will most certainly appreciate the feedback.
Profile ID: LFWR-SCP-O-601485