Intertwining operators associated to the group

Author:
Charles F. Dunkl

Journal:
Trans. Amer. Math. Soc. **347** (1995), 3347-3374

MSC:
Primary 22E30; Secondary 20B30, 33C50, 33C80

DOI:
https://doi.org/10.1090/S0002-9947-1995-1316848-8

MathSciNet review:
1316848

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Abstract | References | Similar Articles | Additional Information

Abstract: For any finite reflection group on an Euclidean space there is a parametrized commutative algebra of differential-difference operators with as many parameters as there are conjugacy classes of reflections in . There exists a linear isomorphism on polynomials which intertwines this algebra with the algebra of partial differential operators with constant coefficients, for all but a singular set of parameter values (containing only certain negative rational numbers). This paper constructs an integral transform implementing the intertwining operator for the group , the symmetric group on three objects, for parameter value . The transform is realized as an absolutely continuous measure on a compact subset of , which contains the group as a subset of its boundary. The construction of the integral formula involves integration over the unitary group .

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Additional Information

DOI:
https://doi.org/10.1090/S0002-9947-1995-1316848-8

Keywords:
Dunkl operators,
intertwining operator,
reflection groups,
integral transform

Article copyright:
© Copyright 1995
American Mathematical Society