Zobrazeno 1 - 10
of 79
pro vyhledávání: '"Gaboriaud, Julien"'
New bivariate Griffiths polynomials of $q$-Racah type are introduced and characterized. They generalize the polynomials orthogonal on the multinomial distribution introduced by R. Griffiths fifty years ago. They also correspond to a $q$-deformation o
Externí odkaz:
http://arxiv.org/abs/2407.17016
Bivariate Griffiths polynomials of Racah type are constructed from univariate Racah polynomials. The bispectral properties of the former are deduced from simple properties of the latter. A duality relation and the orthogonality of these polynomials a
Externí odkaz:
http://arxiv.org/abs/2403.12148
We compute the matrix elements of $SO(3)$ in any finite-dimensional irreducible representation of $sl_3$. They are expressed in terms of a double sum of products of Krawtchouk and Racah polynomials which generalize the Griffiths-Krawtchouk polynomial
Externí odkaz:
http://arxiv.org/abs/2308.12809
Autor:
Gaboriaud, Julien
Cette thèse se divise en trois parties qui peuvent être toutes regroupées autour d'une même bannière : l'étude de structures algébriques reliées aux algèbres de type Askey–Wilson. Alors que dans la première partie on s'efforce d'obtenir d
We introduce families of rational functions that are biorthogonal with respect to the $q$-hypergeometric distribution. A triplet of $q$-difference operators $X$, $Y$, $Z$ is shown to play a role analogous to the pair of bispectral operators of orthog
Externí odkaz:
http://arxiv.org/abs/2202.05925
Publikováno v:
Ann. Henri Poincar\'e 23 (2022), no. 7, 2657--2682
The higher rank Racah algebra $R(n)$ introduced recently is recalled. A quotient of this algebra by central elements, which we call the special Racah algebra $sR(n)$, is then introduced. Using results from classical invariant theory, this $sR(n)$ alg
Externí odkaz:
http://arxiv.org/abs/2105.01086
Autor:
Beaudoin, André, Bergeron, Geoffroy, Brillant, Antoine, Gaboriaud, Julien, Vinet, Luc, Zhedanov, Alexei
We consider the unital associative algebra $\mathcal{A}$ with two generators $\mathcal{X}$, $\mathcal{Z}$ obeying the defining relation $[\mathcal{Z},\mathcal{X}]=\mathcal{Z}^2+\Delta$. We construct irreducible tridiagonal representations of $\mathca
Externí odkaz:
http://arxiv.org/abs/2104.13960
The relation between Wilson and para-Racah polynomials and representations of the degenerate rational Sklyanin algebra is established. Second order Heun operators on quadratic grids with no diagonal terms are determined. These special or S-Heun opera
Externí odkaz:
http://arxiv.org/abs/2103.09631
Autor:
Crampé, Nicolas, Frappat, Luc, Gaboriaud, Julien, d'Andecy, Loïc Poulain, Ragoucy, Eric, Vinet, Luc
Publikováno v:
J. Phys. A 54 (2021), no. 6, Paper No. 063001, 32 pp
The original Askey-Wilson algebra introduced by Zhedanov encodes the bispectrality properties of the eponym polynomials. The name 'Askey-Wilson algebra' is currently used to refer to a variety of related structures that appear in a large number of co
Externí odkaz:
http://arxiv.org/abs/2009.14815
S-Heun operators on linear and $q$-linear grids are introduced. These operators are special cases of Heun operators and are related to Sklyanin-like algebras. The Continuous Hahn and Big $q$-Jacobi polynomials are functions on which these S-Heun oper
Externí odkaz:
http://arxiv.org/abs/2008.03266