73 citations · 480 across the 42 of their papers we have counts for
7 papers · 1 filter
Generalised symmetries and bases for Dunkl monogenics
Hendrik De Bie, Alexis Langlois-Rémillard, Roy Oste +1
We introduce a family of commuting generalised symmetries of the Dunkl--Dirac operator inspired by the Maxwell construction in harmonic analysis. We use these generalised symmetrie…
Finite-dimensional representations of the symmetry algebra of the dihedral Dunkl--Dirac operator
Hendrik De Bie, Alexis Langlois-Rémillard, Roy Oste +1
The Dunkl--Dirac operator is a deformation of the Dirac operator by means of Dunkl derivatives. We investigate the symmetry algebra generated by the elements supercommuting with th…
Deformations of unitary Howe dual pairs
Dan Ciubotaru, Hendrik De Bie, Marcelo De Martino +1
We study deformations of the Howe dual pairs and to the context of a rational Cherednik algebra $H_{1,c}(G,E…
The Racah algebra: An overview and recent results
Hendrik De Bie, Plamen Iliev, Wouter van de Vijver +1
Recent results on the Racah algebra of rank are reviewed. is defined in terms of generators and relations and sits in the centralizer of the…
Bannai-Ito algebras and the superalgebra
Hendrik De Bie, Vincent X. Genest, Wouter van de Vijver +1
The Bannai-Ito algebra of rank is defined as the algebra generated by the Casimir operators arising in the -fold tensor product of the superalgebra. Th…
The harmonic transvector algebra in two vector variables
Hendrik De Bie, David Eelbode, Matthias Roels
The decomposition of polynomials of one vector variable into irreducible modules for the orthogonal group is a crucial result in harmonic analysis which makes use of the Howe duali…