Zobrazeno 1 - 10
of 64
pro vyhledávání: '"Hendrik De Bie"'
Publikováno v:
Acta Polytechnica, Vol 56, Iss 3, Pp 166-172 (2016)
A quantum superintegrable model with reflections on the three-sphere is presented. Its symmetry algebra is identified with the rank-two Bannai-Ito algebra. It is shown that the Hamiltonian of the system can be constructed from the tensor product of f
Externí odkaz:
https://doaj.org/article/c20ded7dbef44a33a278c67370f429a9
Publikováno v:
Symmetry, Integrability and Geometry: Methods and Applications, Vol 9, p 010 (2013)
This paper is a continuation of the paper [De Bie H., Ørsted B., Somberg P., Souček V., Trans. Amer. Math. Soc. 364 (2012), 3875–3902], investigating a natural radial deformation of the Fourier transform in the setting of Clifford analysis. At th
Externí odkaz:
https://doaj.org/article/e279aed544b4404daaba33fe9e881f52
Autor:
Hendrik De Bie
Publikováno v:
Symmetry, Integrability and Geometry: Methods and Applications, Vol 4, p 093 (2008)
We introduce the so-called Clifford-Hermite polynomials in the framework of Dunkl operators, based on the theory of Clifford analysis. Several properties of these polynomials are obtained, such as a Rodrigues formula, a differential equation and an e
Externí odkaz:
https://doaj.org/article/cbb65c2882b44a0fba976820bceda8b5
Publikováno v:
JOURNAL OF ALGEBRA
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 the Dunkl--Dirac operator and its dual symbol. This symmetry algebra is
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::fe3a38f81ed9c78d77b9cd5af3867533
https://doi.org/10.1016/j.jalgebra.2021.09.025
https://doi.org/10.1016/j.jalgebra.2021.09.025
Publikováno v:
Lie Groups, Number Theory, and Vertex Algebras. :3-20
Recent results on the Racah algebra $\mathcal{R}_n$ of rank $n - 2$ are reviewed. $\mathcal{R}_n$ is defined in terms of generators and relations and sits in the centralizer of the diagonal action of $\mathfrak{su}(1,1)$ in $\mathcal{U}(\mathfrak{su}
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::483f08995a80027263cca2db643efce7
https://doi.org/10.1090/conm/768/15450
https://doi.org/10.1090/conm/768/15450
Publikováno v:
JOURNAL OF GEOMETRIC ANALYSIS
The monogenic Hua-Radon transform is defined as an orthogonal projection on holomorphic functions in the Lie sphere. Extending the work of Sabadini and Sommen (J Geom Anal 29:2709-2737, 2019), we determine its reproducing kernel. Integrating this ker
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::c9a51d8d1b143a512c23960c12d56a6e
https://doi.org/10.1007/s12220-021-00749-3
https://doi.org/10.1007/s12220-021-00749-3
Publikováno v:
Symmetry, Integrability and Geometry: Methods and Applications.
We study a particular class of infinite-dimensional representations of $\mathfrak{osp}(1|2n)$. These representations $L_n(p)$ are characterized by a positive integer $p$, and are the lowest component in the $p$-fold tensor product of the metaplectic
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_________::1160d77bf1118ff051d845e05ec0ac85
https://doi.org/10.3842/sigma.2021.031
https://doi.org/10.3842/sigma.2021.031
Publikováno v:
Journal of Mathematical Analysis and Applications
JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS
JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS
By exploiting the Fueter theorem, we give new formulas to compute zonal harmonic functions in any dimension. We first give a representation of them as a result of a suitable ladder operator acting on the constant function equal to one. Then, inspired
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::2d7a268af58651d50ffb5cd965d68506
https://gfzpublic.gfz-potsdam.de/pubman/item/item_5009964
https://gfzpublic.gfz-potsdam.de/pubman/item/item_5009964
Autor:
Hadewijch De Clercq, Hendrik De Bie
Publikováno v:
JOURNAL OF THE LONDON MATHEMATICAL SOCIETY-SECOND SERIES
The Gasper and Rahman multivariate $(-q)$-Racah polynomials appear as connection coefficients between bases diagonalizing different abelian subalgebras of the recently defined higher rank $q$-Bannai-Ito algebra $\mathcal{A}_n^q$. Lifting the action o
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::e32cbadf30142894971311b7aa1ba69a
https://biblio.ugent.be/publication/8758251
https://biblio.ugent.be/publication/8758251
Publikováno v:
SYMMETRY INTEGRABILITY AND GEOMETRY-METHODS AND APPLICATIONS
The minimal representation of a semisimple Lie group is a 'small' infinite-dimensional irreducible unitary representation. It is thought to correspond to the minimal nilpotent coadjoint orbit in Kirillov's orbit philosophy. The Segal-Bargmann transfo
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::22101692a389b1b5f34aef3fa1678186
https://doi.org/10.3842/sigma.2020.085
https://doi.org/10.3842/sigma.2020.085