Remote Access Transactions of the American Mathematical Society
Green Open Access

Transactions of the American Mathematical Society

ISSN 1088-6850(online) ISSN 0002-9947(print)



Intertwining operators associated to the group $ S\sb 3$

Author: Charles F. Dunkl
Journal: Trans. Amer. Math. Soc. 347 (1995), 3347-3374
MSC: Primary 22E30; Secondary 20B30, 33C50, 33C80
MathSciNet review: 1316848
Full-text PDF

Abstract | References | Similar Articles | Additional Information

Abstract: For any finite reflection group $ G$ 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 $ G$. 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 $ {S_3}$, the symmetric group on three objects, for parameter value $ \geqslant \frac{1} {2}$. The transform is realized as an absolutely continuous measure on a compact subset of $ {M_2}({\mathbf{R}})$, which contains the group as a subset of its boundary. The construction of the integral formula involves integration over the unitary group $ U(3)$.

References [Enhancements On Off] (What's this?)

Similar Articles

Retrieve articles in Transactions of the American Mathematical Society with MSC: 22E30, 20B30, 33C50, 33C80

Retrieve articles in all journals with MSC: 22E30, 20B30, 33C50, 33C80

Additional Information

Keywords: Dunkl operators, intertwining operator, reflection groups, integral transform
Article copyright: © Copyright 1995 American Mathematical Society

American Mathematical Society