Classical W-algebras in types A, B, C, D and G

Abstract

We produce explicit generators of the classical W-algebras associated with the principal nilpotents in the simple Lie algebras of all classical types and in the exceptional Lie algebra of type $G_2$. The generators are given by determinant formulas in the context of the Poisson vertex algebras. We also show that the images of the W-algebra generators under the Chevalley-type isomorphism coincide with the elements defined via the corresponding Miura transformations.

arXiv comment37 pages

References in corpus (11)

• W-symmetry in Conformal Field Theory
• Noncommutative symmetric functions
• Quantum spectral curves, quantum integrable systems and the geometric Langlands correspondence
• On higher order Sugawara operators
• Classical W-algebras and generalized Drinfeld-Sokolov bi-Hamiltonian systems within the theory of Poisson vertex algebras
• Feigin-Frenkel center in types B, C and D
• Explicit generators in rectangular affine W-algebras of type A
• Folding the W Algebras
• On classical finite and affine W-algebras
• Dirac operators and the Very Strange Formula for Lie superalgebras
• Yangian characters and classical W-algebras

Cited by in corpus (6)

• Classical W-algebras for gl_N and associated integrable Hamiltonian hierarchies
• Explicit generators in rectangular affine W-algebras of type A
• Classical affine W-algebras and the associated integrable Hamiltonian hierarchies for classical Lie algebras
• Segal-Sugawara vectors for the Lie algebra of type $G_2$
• Generators of Supersymmetric Classical $W$-algebras
• Classical $\mathcal{W}$-algebras for centralizers