Partially-massless higher spin algebras in four dimensions
T Basile, S Dhasmana - arXiv preprint arXiv:2407.11884, 2024 - arxiv.org
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 …
terms of bosonic and fermionic oscillators, using Howe duality between $ sp (4,\mathbb …
[HTML][HTML] The centre of the Dunkl total angular momentum algebra
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 …
rational Cherednik algebra H t, c (V, W) associated with (V, W) at the parameters t≠ 0 and c …
Supercentralizers for deformations of the Pin osp dual pair
R Oste - arXiv preprint arXiv:2110.15337, 2021 - arxiv.org
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 …
supercommuting with realization of the Lie superalgebra $\mathfrak {osp}(1| 2) $ inside a …
Dirac operators for the Dunkl angular momentum algebra
K Calvert, M De Martino - SIGMA. Symmetry, Integrability and Geometry …, 2022 - emis.de
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 …
on certain central elements of the group algebra of the Pin cover of the Weyl group inherent …
Finite-dimensional representations of the symmetry algebra of the dihedral Dunkl–Dirac operator
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 …
derivatives. We investigate the symmetry algebra generated by the elements …
The double dihedral Dunkl total angular momentum algebra
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 …
superalgebra inside the tensor product of a rational Cherednik algebra and a Clifford …
Two invariant subalgebras of rational Cherednik algebras
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 …
rational Cherednik algebra have been considered in the literature. The first is the …
[PDF][PDF] Topics in representation theory of the Dunkl total angular momentum algebra
A Langlois-Rémillard - 2023 - alexisl-r.github.io
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 …
the people infusing life in the theory. Subjects are studied and established from sparks and …
Deformations of unitary Howe dual pairs
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 …
$(\mathrm {U}(n),\mathfrak {u}(2| 1)) $ to the context of a rational Cherednik algebra $ H_ {1 …