Computation of monodromy of certain W-invariant local systems of types B, C, D
\textit{V. G. Knizhnik} and \textit{A. B. Zamolodchikov} [Nucl. Phys. B 247, 83-103 (1984; Zbl 0661.17020)] constructed a differential equation important in 2-dimensional models of statistical physics. It is related with braid groups and monodromy representations for them are constructed by \textit{A. Tsuchiya} and \textit{Y. Kanie} [Symp., Kyoto/Jap. 1986, Adv. Stud. Pure Math. 16, 297-372 (1988; Zbl 0661.17021)]. The author showed that the above n-point Knizhnik-Zamolodchikov equation corresponds to root patterns of type A and constructed similar equations for any root system [Dokl. Akad. Nauk SSSR 307, No.1, 49-53 (1989)]. In the paper under review he generalizes the results of Tsuchiya and Kanie to the series B, C, D. In these cases the role of the Hecke algebra is played by the affine Hecke algebra.
scientific article; zbMATH DE number 4181614