Zobrazeno 1 - 10
of 348
pro vyhledávání: '"P. Frappat"'
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 introduce a generalization of bivariate Griffiths polynomials depending on an additional parameter $\lambda$. These $\lambda$-Griffiths polynomials are bivariate, bispectral and biorthogonal. For two specific values of the parameter $\lambda$, the
Externí odkaz:
http://arxiv.org/abs/2311.03256
Publikováno v:
SciPost Phys. 15, 228 (2023)
We provide a closed Poisson algebra involving the Ragnisco--Bruschi generalization of peakon dynamics in the Camassa--Holm shallow-water equation. This algebra is generated by three independent matrices. From this presentation, we propose a one-param
Externí odkaz:
http://arxiv.org/abs/2309.08412
Publikováno v:
SIGMA 19 (2023), 077, 36 pages
We propose a definition by generators and relations of the rank $n-2$ Askey-Wilson algebra $\mathfrak{aw}(n)$ for any integer $n$, generalising the known presentation for the usual case $n=3$. The generators are indexed by connected subsets of $\{1,\
Externí odkaz:
http://arxiv.org/abs/2303.17677
Publikováno v:
Linear Algebra and Its Applications 664 (2023) 165-215
The algebraic structure of the rank two Racah algebra is studied in detail. We provide an automorphism group of this algebra, which is isomorphic to the permutation group of five elements. This group can be geometrically interpreted as the symmetry o
Externí odkaz:
http://arxiv.org/abs/2206.01031
We propose realizations of the Poisson structures for the Lax representations of three integrable $n$-body peakon equations, Camassa--Holm, Degasperis--Procesi and Novikov. The Poisson structures derived from the integrability structures of the conti
Externí odkaz:
http://arxiv.org/abs/2203.13593
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
Publikováno v:
SIGMA 16 (2020), 094, 18 pages
We present a systematic derivation of the abelianity conditions for the $q$-deformed $W$-algebras constructed from the elliptic quantum algebra $\mathcal{A}_{q,p}\big(\widehat{\mathfrak{gl}}(N)_{c}\big)$. We identify two sets of conditions on a given
Externí odkaz:
http://arxiv.org/abs/2005.03579
Publikováno v:
SciPost Phys. 8, 033 (2020)
The algebraic structure underlying the classical $r$-matrix formulation of the complex sine-Gordon model is fully elucidated. It is characterized by two matrices $a$ and $s$, components of the $r$ matrix as $r=a-s$. They obey a modified classical ref
Externí odkaz:
http://arxiv.org/abs/1911.06720