Classical $${\mathcal{W}}$$ W -Algebras in Types A, B, C, D and G

Higher dimensional classical W - algebras

Classical W -algebras in higher dimensions are constructed. This is achieved by generalizing the classical Gel’fand-Dickey brackets to the commutative limit of the ring of classical pseudodifferential operators in arbitrary dimension. These W -algebras are the Poisson structures associated with a higher dimensional version of the Khokhlov-Zabolotskaya hierarchy (dispersionless KP-hierarchy). Th...

A B C d e f g ...

Yangian characters and classical W-algebras

The Yangian characters (or q-characters) are known to be closely related to the classical W-algebras and to the centers of the affine vertex algebras at the critical level. We make this relationship more explicit by producing families of generators of the W-algebras from the characters of the Kirillov–Reshetikhin modules associated with multiples of the first fundamental weight in types B and D...

Vaccination .B. C. G

This article was presented by the author at the Vaccination Seminar of May 26, 1972, National University Medical School.

Feigin–Frenkel center in types B, C and D

For each simple Lie algebra g consider the corresponding affine vertex algebra Vcrit(g) at the critical level. The center of this vertex algebra is a commutative associative algebra whose structure was described by a remarkable theorem of Feigin and Frenkel about two decades ago. However, only recently simple formulas for the generators of the center were found for the Lie algebras of type A fo...