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arXiv · 1401.4960

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

D. V. Artamonov·V. A. Golubeva
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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.

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D. V. Artamonov, V. A. Golubeva. 2014-01-20. $W$-algebras and higher analogs of the Kniznik-Zamolodchikov equations. https://doi.org/10.4213/tmf8644

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