Singular polynomials for finite reflection groups

Dunkl, C. F.; de Jeu, M. F. E.; Opdam, E. M.

doi:10.1090/S0002-9947-1994-1273532-6

Singular polynomials for finite reflection groups
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by C. F. Dunkl, M. F. E. de Jeu and E. M. Opdam

Trans. Amer. Math. Soc. 346 (1994), 237-256

DOI: https://doi.org/10.1090/S0002-9947-1994-1273532-6

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Abstract:

The Dunkl operators involve a multiplicity function as parameter. For generic values of this function the simultaneous kernel of these operators, acting on polynomials, is equal to the constants. For special values, however, this kernel is larger. We determine these singular values completely and give partial results on the representations of $G$ that occur in this kernel.

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