Zobrazeno 1 - 10
of 43
pro vyhledávání: '"d'Andecy, Loïc Poulain"'
We study framizations of algebras through the idea of Schur--Weyl duality. We provide a general setting in which framizations of algebras such as the Yokonuma--Hecke algebra naturally appear and we obtain this way a Schur--Weyl duality for many examp
Externí odkaz:
http://arxiv.org/abs/2312.14796
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
We prove an infinite family of identities satisfied by the Rankin-Cohen brackets involving the Racah polynomials. A natural interpretation in the representation theory of sl(2) is provided. From these identities and known properties of the Racah poly
Externí odkaz:
http://arxiv.org/abs/2304.10803
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:
Ann. Henri Poincar\'e 24 (2023) 1897--1922
A presentation of the centralizer of the three-fold tensor product of the spin $s$ representation of the quantum group $U_q(\mathfrak{sl}_2)$ is provided. It is expressed as a quotient of the Askey-Wilson braid algebra. This newly defined algebra com
Externí odkaz:
http://arxiv.org/abs/2206.11150
Autor:
Bernard, Pierre-Antoine, Crampé, Nicolas, Nepomechie, Rafael I., Parez, Gilles, d'Andecy, Loïc Poulain, Vinet, Luc
Publikováno v:
Nuclear Physics B 984 (2022) 115975
We introduce an inhomogeneous model of free fermions on a $(D-1)$-dimensional lattice with $D(D-1)/2$ continuous parameters that control the hopping strength between adjacent sites. We solve this model exactly, and find that the eigenfunctions are gi
Externí odkaz:
http://arxiv.org/abs/2206.06509
Publikováno v:
Commun. Math. Phys. 400 (2023) 179--213
We present explicit formulas for the operators providing missing labels for the tensor product of two irreducible representations of $\mathfrak{su}_3$. The result is seen as a particular representation of the diagonal centraliser of $\mathfrak{su}_3$
Externí odkaz:
http://arxiv.org/abs/2110.03521
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:
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:
Trans. Amer. Math. Soc. 373 (2020), no. 7, 4907--4932
In the spirit of the Schur-Weyl duality, we study the connections between the Racah algebra and the centralizers of tensor products of three (possibly different) irreducible representations of su(2). As a first step we show that the Racah algebra alw
Externí odkaz:
http://arxiv.org/abs/1905.06346