Singular Polynomials for Finite Reflection Groups
Open Access
- 1 November 1994
- journal article
- Published by JSTOR in Transactions of the American Mathematical Society
- Vol. 346 (1), 237-256
- https://doi.org/10.2307/2154950
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 that occur in this kernel.Keywords
This publication has 10 references indexed in Scilit:
- Differential-difference operators and monodromy representations of Hecke algebrasPacific Journal of Mathematics, 1993
- Integral Kernels with Reflection Group InvarianceCanadian Journal of Mathematics, 1991
- A Remark on the Dunkl Differential—Difference OperatorsPublished by Springer Science and Business Media LLC ,1991
- Irreducible projective modules of the Hecke algebras of a finite coxeter groupJournal of Algebra, 1989
- Differential-Difference Operators Associated to Reflection GroupsTransactions of the American Mathematical Society, 1989
- On the semisimplicity of Hecke algebrasJournal of the Mathematical Society of Japan, 1989
- Reflection groups and orthogonal polynomials on the sphereMathematische Zeitschrift, 1988
- Blocks and Idempotents of Hecke Algebras of General Linear GroupsProceedings of the London Mathematical Society, 1987
- Representations of Hecke Algebras of General Linear GroupsProceedings of the London Mathematical Society, 1986
- Regular elements of finite reflection groupsInventiones Mathematicae, 1974