We propose a realisation of partially-massless higher spin algebras in four dimensions in
terms of bosonic and fermionic oscillators, using Howe duality between $ sp (4,\mathbb …

For a finite dimensional representation V of a finite reflection group W, we consider the
rational Cherednik algebra H t, c (V, W) associated with (V, W) at the parameters t≠ 0 and c …

In recent work, we examined the algebraic structure underlying a class of elements
supercommuting with realization of the Lie superalgebra $\mathfrak {osp}(1| 2) $ inside a …

We define a family of Dirac operators for the Dunkl angular momentum algebra depending
on certain central elements of the group algebra of the Pin cover of the Weyl group inherent …

Abstract 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 …

The Dunkl deformation of the Dirac operator is part of a realisation of an orthosymplectic Lie
superalgebra inside the tensor product of a rational Cherednik algebra and a Clifford …

Originally motivated by connections to integrable systems, two natural subalgebras of the
rational Cherednik algebra have been considered in the literature. The first is the …

Mathematics does not happen in a vacuum. Mathematicians, those who do mathematics, are
the people infusing life in the theory. Subjects are studied and established from sparks and …

We study deformations of the Howe dual pairs $(\mathrm {U}(n),\mathfrak {u}(1, 1)) $ and
$(\mathrm {U}(n),\mathfrak {u}(2| 1)) $ to the context of a rational Cherednik algebra $ H_ {1 …