$W$-algebras and higher analogs of the Kniznik-Zamolodchikov equations

Abstract

The key role in the derivation of the Knizhnik-Zamolodchikov equations in the $WZW$-theory is played by the energy-momentum tensor, that is constructed from a central Casimir element of the second order in a universal enveloping algebra of a corresponding Lie algebra. In the paper a possibility of construction of analogs of Knizhnik-Zamolodchikov equations using higher order central elements is investigated. The Gelfand elements of the third order for a simple Lie algebra of series $A$ and Capelli elements of the fourth order for the a simple Lie algebra of series $B$, $D$ are considered. In the first case the construction is not possible a the second case the desired equation is derived.

36 pages

References in corpus (3)

• On sl3 Knizhnik-Zamolodchikov equations and W3 null-vector equations
• Rational Lax operators and their quantization
• $W$-algebras and higher analogs of the Kniznik-Zamolodchikov equations

Cited by in corpus (1)

• $W$-algebras and higher analogs of the Kniznik-Zamolodchikov equations