W-geometry of the Toda systems associated with non-exceptional simple Lie algebras
نویسندگان
چکیده
منابع مشابه
On 1-dimensional Representations of Finite W -algebras Associated to Simple Lie Algebras of Exceptional Type
We consider the finite W -algebra U(g, e) associated to a nilpotent element e ∈ g in a simple complex Lie algebra g of exceptional type. Using presentations obtained through an algorithm based on the PBW-theorem, we verify a conjecture of Premet, that U(g, e) always has a 1-dimensional representation, when g is of type G2, F4, E6 or E7. Thanks to a theorem of Premet, this allows one to deduce t...
متن کاملRepresentations of Finite W -algebras Associated to Simple Lie Algebras of Exceptional Type
We consider the finite W -algebra U(g, e) associated to a nilpotent element e ∈ g in a simple complex Lie algebra g of exceptional type. Using presentations obtained through an algorithm based on the PBW-theorem, we verify a conjecture of Premet, that U(g, e) always has a 1-dimensional representation, when g is of type G2, F4, E6 or E7. Thanks to a theorem of Premet, this allows one to deduce t...
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We construct the classical W -algebras for some non-abelian Toda systems associated with the Lie groups GL 2n(R) and Spn(R). We start with the set of characteristic integrals and find the Poisson brackets for the corresponding Hamiltonian counterparts. The convenient block matrix representation for the Toda equations is used. The infinitesimal symmetry transformations generated by the elements ...
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Models of all the gradings on the exceptional simple Lie algebras induced by Jordan subgroups of their groups of automorphisms are provided.
متن کامل2 W - algebras for non - abelian Toda systems
We construct the classical W -algebras for some non-abelian Toda systems associated with the Lie groups GL 2n(R) and Spn(R). We start with the set of characteristic integrals and find the Poisson brackets for the corresponding Hamiltonian counterparts. The convenient block matrix representaion for the Toda equations is used. The infinitesimal symmetry transformations generated by the elements o...
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ژورنال
عنوان ژورنال: Communications in Mathematical Physics
سال: 1996
ISSN: 0010-3616,1432-0916
DOI: 10.1007/bf02099714