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Dunkl Operators for Complex Reflection Groups 总被引:3,自引:0,他引:3
Dunkl operators for complex reflection groups are defined inthis paper. These commuting operators give rise to a parameterizedfamily of deformations of the polynomial De Rham complex. Thisleads to the study of the polynomial ring as a module over therational Cherednik algebra, and a natural contravariantform on this module. In the case of the imprimitive complexreflection groups G(m, p, N), the set of singular parametersin the parameterized family of these structures is describedexplicitly, using the theory of non-symmetric Jack polynomials.2000 Mathematical Subject Classification: 20F55 (primary), 52C35,05E05, 33C08 (secondary). 相似文献
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For a given subset E of the natural numbers it is desired to maximize Σn?Ean subject to an?0, 1+Σn?Ean cosnθ?0 for θ?[0,π]. A dual program is defined, and a duality principle is established. Extensions to other series of functions are given, and these include the motivating example of P. Delsarte [Philips Res. Repts.27 (1972), 272–289]. 相似文献
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