Dunkl Operators for Complex Reflection Groups

By Charles F. Dunkl, E. Opdam. 2001

154 citations recorded by the source corpus.

Dunkl operators for complex reflection groups are defined in this paper. These commuting operators give rise to a parameterized family of deformations of the polynomial De Rham complex. This leads to the study of the polynomial ring as a module over the ‘rational Cherednik algebra’, and a natural contravariant form on this module. In the case of the imprimitive complex reflection groups G(m, p, N), the set of singular parameters in the parameterized family of these structures is described explicitly, using the theory of non‐symmetric Jack polynomials. 2000 Mathematical Subject Classification: 20F55 (primary), 52C35, 05E05, 33C08 (secondary).

Subfields: Algebra and Number Theory, Geometry and Topology, Statistical and Nonlinear Physics

View Paper: https://www.semanticscholar.org/paper/79bd1e412cab4a938244dd88e6c923be423e3b77

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In Algebra and Number Theory

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In Statistical and Nonlinear Physics

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Citations in the corpus

• Orthogonal functions generalizing Jack polynomials (2007, methodology): “, ∅ one obtains the polynomials discovered in section 3 of (9) (which are a slight modification of non-symmetric Jack polynomials).”
• Geometric representations of graded and rational Cherednik algebras (2014, background): “The papers [14] and [7] initiated the study of the representation theory of these algebras.”