Dunkl-Type Operators with Projection Terms Associated to Orthogonal Subsystems in Root System

• Published in: Symmetry, Integrability and Geometry: Methods and Applications
• Date: 2013
• ISSN: 1815-0659
• Main Author: Bouzeffour, F.
• Format: Article
• Language: English
• Published: Інститут математики НАН України 2013
• Online Access: https://nasplib.isofts.kiev.ua/handle/123456789/149356
• Journal Title: Digital Library of Periodicals of National Academy of Sciences of Ukraine
• Cite this: Dunkl-Type Operators with Projection Terms Associated to Orthogonal Subsystems in Root System / F. Bouzeffour // Symmetry, Integrability and Geometry: Methods and Applications. — 2013. — Т. 9. — Бібліогр.: 15 назв. — англ.

In this paper, we introduce a new differential-difference operator Tξ (ξ∈RN) by using projections associated to orthogonal subsystems in root systems. Similarly to Dunkl theory, we show that these operators commute and we construct an intertwining operator between Tξ and the directional derivative ∂...