Lie algebras and equations of Korteweg-de Vries type

Geometry of 2D topological field theories

“…Chazy considered also the equation 000 6 00 + 9 0 2 + 432 n 2 36 0 1 2 2 2 = 0 ( C: 41) for an integer n > 6. The correspondent Lame equation y 00 m(m + 1 ) } 0 ( x ) y = 0 ( C:42) has m = 3 n 1 2 : (C:43)…”

Primary currents and Riemannian geometry in algebras

“…Using successively (2.5), Leibniz rule and (2.10) one gets after some combinatoric manipulations 13) with the polynomial in the a (s)…”

Drinfeld-Sokolov reduction for quantum groups and deformations of W-algebras

“…This coadjoint action is Hamiltonian and has a moment map µ : ( g ′ ) * → n + [z, z −1 ] * = n − [z, z −1 ], where n − is the opposite nilpotent subalgebra in g, and we have identified the space n + [z, z −1 ] * with n − [z, z −1 ] using the standard scalar product on g ′ . The reduced space entering the definition of the algebra W (g) corresponds to the value f of the moment map µ, where f is a regular nilpotent element in n − ⊂ n − [z, z −1 ] regarded as a Lie subalgebra in g. The reduction procedure described above was introduced in [14] and is called now the Drinfeld-Sokolov reduction procedure.…”