Provably fair representations
Machine learning systems are increasingly used to make decisions about people's lives,
such as whether to give someone a loan or whether to interview someone for a job. This has …
such as whether to give someone a loan or whether to interview someone for a job. This has …
Z2× Z2 generalizations of 𝒩= 2 super Schrödinger algebras and their representations
We generalize the real and chiral N= 2 super Schrödinger algebras to Z 2× Z 2-graded Lie
superalgebras. This is done by D-module presentation, and as a consequence, the D …
superalgebras. This is done by D-module presentation, and as a consequence, the D …
Dunkl symplectic algebra in generalized Calogero models
T Hakobyan - arXiv preprint arXiv:2306.17677, 2023 - arxiv.org
We study the properties of the symplectic sp (2N) algebra deformed by means of the Dunkl
operators, which describe the dynamical symmetry of the generalized N-particle Calogero …
operators, which describe the dynamical symmetry of the generalized N-particle Calogero …
[HTML][HTML] The centre of the Dunkl total angular momentum algebra
K Calvert, M De Martino, R Oste - Journal of Algebra, 2024 - Elsevier
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 …
[HTML][HTML] Algebra of Dunkl Laplace–Runge–Lenz vector
M Feigin, T Hakobyan - Letters in Mathematical Physics, 2022 - Springer
We introduce the Dunkl version of the Laplace–Runge–Lenz vector associated with a finite
Coxeter group W acting geometrically in RN and with a multiplicity function g. This vector …
Coxeter group W acting geometrically in RN and with a multiplicity function g. This vector …
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 …
The ‐Bannai–Ito algebra and multivariate ‐Racah and Bannai–Ito polynomials
H De Bie, H De Clercq - Journal of the London Mathematical …, 2021 - Wiley Online Library
Abstract The Gasper and Rahman multivariate (− q)‐Racah polynomials appear as
connection coefficients between bases diagonalizing different abelian subalgebras of the …
connection coefficients between bases diagonalizing different abelian subalgebras of the …
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 …