Determinantal Construction of Orthogonal Polynomials Associated with Root Systems
Jan Felipe van Diejen, Luc Lapointe, Jennifer Morse
Abstract
We consider semisimple triangular operators acting in the symmetric component of the group algebra over the weight lattice of a root system. We present a determinantal formula for the eigenbasis of such triangular operators. This determinantal formula gives rise to an explicit construction of the Macdonald polynomials and of the Heckman-Opdam generalized Jacobi polynomials.
Create a lesson
Related papers
2-large sets are sets of nil-Bohr recurrence
Ryan Alweiss, Sohail Farhangi
New tools for sparse graph embeddings: Hybrid expanders and application to nested cycles
Nemanja Draganić
Edge and spectral conditions for rainbow bipancyclicity in bipartite graph collections
Lihua You, Xiaoxue Zhang, Xinghui Zhao
The rich-neighbor chromatic index is linear in the maximum degree
Masaki Kashima, Mirko Petruševski, Jelena Sedlar et al.
The (km,kn)-square paths theorem
Dun Qiu, Minhao Zhang
Towards a Sum-of-Squares Proof for the Nonexistence of Conway's 99-graph
Joseph Natal, Oleksiy Al-saadi