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A unification of Knizhnik-Zamolodchikov and Dunkl operators via affine Hecke algebras. (English) Zbl 0725.20012
Some generalizations of the Lusztig-Lascoux-Schützenberger operators for affine Hecke algebras are considered. As corollaries we obtain Lusztig’s isomorphisms from affine Hecke algebras to their degenerate versions, a “natural” interpretation of the Dunkl operators and a new class of differential-difference operators generalizing Dunkl’s ones and the Knizhnik-Zamolodchikov operators from the two dimensional conformal field theory.

MSC:
20C35 Applications of group representations to physics and other areas of science
43A65 Representations of groups, semigroups, etc. (aspects of abstract harmonic analysis)
81T40 Two-dimensional field theories, conformal field theories, etc. in quantum mechanics
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