Geodesic
Noncommutative Pfaffians associated with the orthogonal algebra
Sbornik. Mathematics, Tome 203 (2012) no. 12, pp. 1685-1714

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Commutators of Pfaffians associated with the orthogonal algebra are found in skew-symmetric and root realizations of $\mathfrak{o}_N$. A generating function of Pfaffians is proved to satisfy the reflection equation. A relation between Pfaffians in skew-symmetric and root realizations of $\mathfrak{o}_N$ is established. Using these results we construct an integrable equation of Knizhnik-Zamolodchikov type using the Capelli central elements in $U(\mathfrak{o}_N)$, which are sums of squares of the considered Pfaffians. A classical limit of the obtained Knizhnik-Zamolodchikov type equation turns out to be a very specific system of equations of isomonodromic deformations. Bibliography: 18 titles.
Keywords: noncommutative Pfaffians, central elements, the Knizhnik-Zamolodchikov equation.
Mots-clés : orthogonal algebra, Capelli elements 
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     author = {D. V. Artamonov and V. A. Golubeva},
     title = {Noncommutative {Pfaffians} associated with the orthogonal algebra},
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D. V. Artamonov; V. A. Golubeva. Noncommutative Pfaffians associated with the orthogonal algebra. Sbornik. Mathematics, Tome 203 (2012) no. 12, pp. 1685-1714. http://geodesic.mathdoc.fr/item/SM_2012_203_12_a1/