DUNKL OPERATORS FOR COMPLEX REFLECTION GROUPS
نویسندگان
چکیده
منابع مشابه
Dunkl Operators and Canonical Invariants of Reflection Groups
Using Dunkl operators, we introduce a continuous family of canonical invariants of finite reflection groups. We verify that the elementary canonical invariants of the symmetric group are deformations of the elementary symmetric polynomials. We also compute the canonical invariants for all dihedral groups as certain hypergeometric functions.
متن کاملFusion Algebras for Imprimitive Complex Reflection Groups
We prove that the Fourier matrices for the imprimitive complex reflection groups introduced by Malle in [9] define fusion algebras with not necessarily positive but integer structure constants. Hence they define Z-algebras. As a result, we obtain that all known Fourier matrices belonging to spetses define algebras with integer structure constants.
متن کاملSpringer Theory for Complex Reflection Groups
Many complex reflection groups behave as though they were the Weyl groups of “nonexistent algebraic groups”: one can associate to them various representation-theoretic structures and carry out calculations that appear to describe the geometry and representation theory of an unknown object. This paper is a survey of a project to understand the geometry of the “unipotent variety” of a complex ref...
متن کاملSutherland Models for Complex Reflection Groups
There are known to be integrable Sutherland models associated to every real root system – or, which is almost equivalent, to every real reflection group. Real reflection groups are special cases of complex reflection groups. In this paper we associate certain integrable Sutherland models to the classical family of complex reflection groups. Internal degrees of freedom are introduced, defining d...
متن کاملNonlocal Operational Calculi for Dunkl Operators
The one-dimensional Dunkl operator Dk with a non-negative parameter k, is considered under an arbitrary nonlocal boundary value condition. The right inverse operator of Dk, satisfying this condition is studied. An operational calculus of Mikusiński type is developed. In the frames of this operational calculi an extension of the Heaviside algorithm for solution of nonlocal Cauchy boundary value ...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Proceedings of the London Mathematical Society
سال: 2003
ISSN: 0024-6115,1460-244X
DOI: 10.1112/s0024611502013825