RUS  ENG
Ïîëíàÿ âåðñèÿ
ÆÓÐÍÀËÛ // Symmetry, Integrability and Geometry: Methods and Applications

SIGMA, 2023, òîì 19, 077, 36 ñòð. (Mi sigma1972)

The Higher-Rank Askey–Wilson Algebra and Its Braid Group Automorphisms
Nicolas Crampé, Luc Frappat, Loïc Poulain d'Andecy, Eric Ragoucy

Ñïèñîê ëèòåðàòóðû

1. Bannai E., Ito T., Algebraic combinatorics, v. I, Association schemes, The Benjamin/Cummings Publishing Co., Inc., Menlo Park, CA, 1984  mathscinet  zmath
2. Chen H., On skein algebras of planar surfaces, arXiv: 2206.07856
3. Cooke J., Lacabanne A., Higher rank Askey–Wilson algebras as skein algebras, arXiv: 2205.04414
4. Crampé N., Frappat L., Gaboriaud J., Poulain d'Andecy L., Ragoucy E., Vinet L., “The Askey–Wilson algebra and its avatars”, J. Phys. A, 54 (2021), 063001, 32 pp., arXiv: 2009.14815  crossref  mathscinet  zmath
5. Crampé N., Frappat L., Ragoucy E., “Representations of the rank two Racah algebra and orthogonal multivariate polynomials”, Linear Algebra Appl., 664 (2023), 165–215, arXiv: 2206.01031  crossref  mathscinet
6. Crampé N., Gaboriaud J., Poulain d'Andecy L., Vinet L., “Racah algebras, the centralizer $Z_n(\mathfrak{sl}_2)$ and its Hilbert–Poincaré series”, Ann. Henri Poincaré, 23 (2022), 2657–2682, arXiv: 2105.01086  crossref  mathscinet  zmath
7. Crampé N., Gaboriaud J., Vinet L., Zaimi M., “Revisiting the Askey–Wilson algebra with the universal $R$-matrix of ${\rm U}_q(\mathfrak{sl}_2)$”, J. Phys. A, 53 (2020), 05LT01, 10 pp., arXiv: 1908.04806  crossref  mathscinet  zmath
8. Crampé N., Poulain d'Andecy L., Vinet L., Zaimi M., “Askey–Wilson braid algebra and centralizer of ${\rm U}_q(\mathfrak{sl}_2)$”, Ann. Henri Poincaré, 24 (2023), 1897–1922, arXiv: 2206.11150  crossref  mathscinet
9. Crampé N., Vinet L., Zaimi M., “Temperley–Lieb, Birman–Murakami–Wenzl and Askey–Wilson algebras and other centralizers of ${\rm U}_q(\mathfrak{sl}_2)$”, Ann. Henri Poincaré, 22 (2021), 3499–3528, arXiv: 2008.04905  crossref  mathscinet
10. De Bie H., De Clercq H., “The $q$-Bannai–Ito algebra and multivariate $(-q)$-Racah and Bannai–Ito polynomials”, J. Lond. Math. Soc., 103 (2021), 71–126, arXiv: 1902.07883  crossref  mathscinet  zmath
11. De Bie H., De Clercq H., van de Vijver W., “The higher rank $q$-deformed Bannai–Ito and Askey–Wilson algebra”, Comm. Math. Phys., 374 (2020), 277–316, arXiv: 1805.06642  crossref  mathscinet  zmath
12. De Clercq H., “Higher rank relations for the Askey–Wilson and $q$-Bannai–Ito algebra”, SIGMA, 15 (2019), 099, 32 pp., arXiv: 1908.11654  mathnet  crossref  mathscinet  zmath
13. Genest V.X., Iliev P., Vinet L., “Coupling coefficients of $\mathfrak{su}_q(1,1)$ and multivariate $q$-Racah polynomials”, Nuclear Phys. B, 927 (2018), 97–123, arXiv: 1702.04626  crossref  mathscinet  zmath
14. Genest V.X., Vinet L., Zhedanov A., “Superintegrability in two dimensions and the Racah–Wilson algebra”, Lett. Math. Phys., 104 (2014), 931–952, arXiv: 1307.5539  crossref  mathscinet  zmath
15. Geronimo J.S., Iliev P., “Multivariable Askey–Wilson function and bispectrality”, Ramanujan J., 24 (2011), 273–287  crossref  mathscinet  zmath
16. Granovskii Y.I., Zhedanov A.S., “Nature of the symmetry group of the $6j$-symbol”, J. Exp. Theor. Phys., 67 (1988), 1982–1985  mathscinet
17. Granovskii Y.I., Zhedanov A.S., “Hidden symmetry of the Racah and Clebsch–Gordan problems for the quantum algebra $\mathfrak{sl}_q(2)$”, J. Group Theoret. Methods Phys., 1 (1993), 161–171, arXiv: hep-th/9304138
18. Groenevelt W., “A quantum algebra approach to multivariate Askey–Wilson polynomials”, Int. Math. Res. Not., 2021 (2021), 3224–3266, arXiv: 1809.04327  crossref  mathscinet  zmath
19. Groenevelt W., Wagenaar C., “An Askey–Wilson algebra of rank 2”, SIGMA, 19 (2023), 008, 35 pp., arXiv: 2206.03986  mathnet  crossref  mathscinet
20. Huang H.-W., “Finite-dimensional irreducible modules of the universal Askey–Wilson algebra”, Comm. Math. Phys., 340 (2015), 959–984, arXiv: 1210.1740  crossref  mathscinet  zmath
21. Huang H.-W., “An embedding of the universal Askey–Wilson algebra into ${\rm U}_q(\mathfrak{sl}_2)\otimes {\rm U}_q(\mathfrak{sl}_2)\otimes {\rm U}_q(\mathfrak{sl}_2)$”, Nuclear Phys. B, 922 (2017), 401–434, arXiv: 1611.02130  crossref  mathscinet  zmath
22. Iliev P., “Bispectral commuting difference operators for multivariable Askey–Wilson polynomials”, Trans. Amer. Math. Soc., 363 (2011), 1577–1598, arXiv: 0801.4939  crossref  mathscinet  zmath
23. Kalnins E.G., Kress J.M., Miller Jr. W., “Second-order superintegrable systems in conformally flat spaces. I Two-dimensional classical structure theory”, J. Math. Phys., 46 (2005), 053509, 28 pp.  crossref  mathscinet  zmath
24. Kassel C., Turaev V., Braid groups, Grad. Texts in Math., 247, Springer, New York, 2008  crossref  mathscinet  zmath
25. Leonard D.A., “Orthogonal polynomials, duality and association schemes”, SIAM J. Math. Anal., 13 (1982), 656–663  crossref  mathscinet  zmath
26. Post S., “Models of quadratic algebras generated by superintegrable systems in 2D”, SIGMA, 7 (2011), 036, 20 pp., arXiv: 1104.0734  mathnet  crossref  mathscinet  zmath
27. Post S., Walter A., A higher rank extension of the Askey–Wilson algebra, arXiv: 1705.01860
28. Terwilliger P., “The universal Askey–Wilson algebra”, SIGMA, 7 (2011), 069, 24 pp., arXiv: 1104.2813  mathnet  crossref  mathscinet  zmath
29. Terwilliger P., Vidunas R., “Leonard pairs and the Askey–Wilson relations”, J. Algebra Appl., 3 (2004), 411–426, arXiv: math.QA/0305356  crossref  mathscinet  zmath
30. Vermaseren J.A.M., New features of FORM, https://github.com/vermaseren/form, arXiv: math-ph/0010025
31. Zhedanov A.S., ““Hidden symmetry” of Askey–Wilson polynomials”, Theoret. and Math. Phys., 89 (1991), 1146–1157  mathnet  crossref  mathscinet  zmath


© ÌÈÀÍ, 2026