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.


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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