The Relationship between Zhedanov's Algebra $AW(3)$ and the Double Affine Hecke Algebra in the Rank One Case
Tom H. Koornwinder

Эта публикация цитируется в следующих статьяx:

1. Wanxia Wang, Shilin Yang, “On the Higher-Rank Askey–Wilson Algebras”, SIGMA, 20 (2024), 115, 30 pp.    
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15. Crampe N. van de Vijver W. Vinet L., “Racah Problems For the Oscillator Algebra, the Lie Algebra Sl(N), and Multivariate Krawtchouk Polynomials”, Ann. Henri Poincare, 21:12 (2020), 3939–3971        
16. Crampe N., Gaboriaud J., Vinet L., Zaimi M., “Revisiting the Askey-Wilson Algebra With the Universal R-Matrix of Uq(Sl2)”, J. Phys. A-Math. Theor., 53:5 (2020), 05LT01      
17. De Bie H., De Clercq H., van de Vijver W., “The Higher Rank Q-Deformed Bannai-Ito and Askey-Wilson Algebra”, Commun. Math. Phys., 374:1 (2020), 277–316        
18. Frappat L. Gaboriaud J. Ragoucy E. Vinet L., “The Dual Pair (Uq(Su(1,1)),O(Q1/2)(2N)), Q-Oscillators, and Askey-Wilson Algebras”, J. Math. Phys., 61:4 (2020), 041701        
19. Tsujimoto S. Vinet L. Zhedanov A., “Double Affine Hecke Algebra of Rank 1 and Orthogonal Polynomials on the Unit Circle”, Constr. Approx., 50:2 (2019), 209–241        
20. Baseilhac P., Crampe N., “Frt Presentation of Classical Askey-Wilson Algebras”, Lett. Math. Phys., 109:10 (2019), 2187–2207        
21. Hikami K., “Daha and Skein Algebra of Surfaces: Double-Torus Knots”, Lett. Math. Phys., 109:10 (2019), 2305–2358      
22. Tsujimoto S. Vinet L. Yu G.-F. Zhedanov A., “Symmetric Abstract Hypergeometric Polynomials”, J. Math. Anal. Appl., 458:1 (2018), 742–754          
23. Mazzocco M., “Embedding of the Rank 1 Daha Into Mat(2, T-Q) and Its Automorphisms”, Representation Theory, Special Functions and Painleve Equations - Rims 2015, Advanced Studies in Pure Mathematics, 76, ed. Konno H. Sakai H. Shiraishi J. Suzuki T. Yamada Y., Math Soc Japan, 2018, 449–468      
24. Koornwinder T.H., Mazzocco M., “Dualities in the Q-Askey Scheme and Degenerate Daha”, Stud. Appl. Math., 141:4, SI (2018), 424–473          
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27. Nomura K. Terwilliger P., “The Universal DAHA of Type (C-1(V), C-1) and Leonard pairs of Q-Racah Type”, Linear Alg. Appl., 533 (2017), 14–83          
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31. Genest V.X. Vinet L. Zhedanov A., “The Quantum Superalgebra
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32. Sarah Post, “Racah Polynomials and Recoupling Schemes of $\mathfrak{su}(1,1)$”, SIGMA, 11 (2015), 057, 17 pp.      
33. Genest V.X., Vinet L., Zhedanov A., “the Equitable Presentation of Osp(Q)(1 Vertical Bar 2) and a Q-Analog of the Bannai–Ito Algebra”, Lett. Math. Phys., 105:12 (2015), 1725–1734              
34. Huang H.-W., “Finite-Dimensional Irreducible Modules of the Universal Askey–Wilson Algebra”, Commun. Math. Phys., 340:3 (2015), 959–984              
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36. Marta Mazzocco, “Non-Symmetric Basic Hypergeometric Polynomials and Representation Theory for Confluent Cherednik Algebras”, SIGMA, 10 (2014), 116, 10 pp.      
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38. Paul Terwilliger, “The Universal Askey–Wilson Algebra and DAHA of Type $(C_1^{\vee},C_1)$”, SIGMA, 9 (2013), 047, 40 pp.      
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41. Paul Terwilliger, “The Universal Askey–Wilson Algebra”, SIGMA, 7 (2011), 069, 24 pp.      
42. Ito T., Nomura K., Terwilliger P., “A classification of sharp tridiagonal pairs”, Linear Algebra Appl, 435:8 (2011), 1857–1884            
43. Paul Terwilliger, “The Universal Askey–Wilson Algebra and the Equitable Presentation of $U_q(\mathfrak{sl}_2)$”, SIGMA, 7 (2011), 099, 26 pp.      
44. Aneva, B., “Common structures of quantum field theories and lattice systems through boundary symmetry”, Physics of Particles and Nuclei Letters, 8:3 (2011), 282–292        
45. Nomura K., Terwilliger P., “On the shape of a tridiagonal pair”, Linear Algebra and Its Applications, 432:2–3 (2010), 615–636          
46. Tatsuro Ito, Paul Terwilliger, “Double Affine Hecke Algebras of Rank 1 and the $\mathbb Z_3$-Symmetric Askey–Wilson Relations”, SIGMA, 6 (2010), 065, 9 pp.      
47. Aneva B., “Exact solvability of interacting many body lattice systems”, Physics of Particles and Nuclei, 41:4 (2010), 471–507        
48. Kalnins E.G., Miller W. Jr., Post S., “Models for the 3D Singular Isotropic Oscillator Quadratic Algebra”, Phys Atomic Nuclei, 73:2 (2010), 359–366          
49. Tom H. Koornwinder, “Zhedanov's Algebra $AW(3)$ and the Double Affine Hecke Algebra in the Rank One Case. II. The Spherical Subalgebra”, SIGMA, 4 (2008), 052, 17 pp.        
50. Boyka Aneva, “Tridiagonal Symmetries of Models of Nonequilibrium Physics”, SIGMA, 4 (2008), 056, 16 pp.        
51. Aneva, B, “From quantum affine symmetry to the boundary Askey–Wilson algebra and the reflection equation”, Journal of Physics A-Mathematical and Theoretical, 41:13 (2008), 135201