(C1∨,C1) and Leonard triples
References
- Cherednik, I. (1992). Double affine Hecke algebras, Knizhnik–Zamolodchikov equations, and Macdonald’s operators. Int. Math. Res. Not. 9:171–180.
- Cherednik, I. (1995). Double affine Hecke algebras and Macdonald’s conjectures. Ann. Math. 141:191–216.
- Curtin, B. (2007). Modular Leonard triples. Linear Algebra Appl. 424(2–3):510–539. DOI: 10.1016/j.laa.2007.02.024.
- Huang, H.-W. (2020). Finite-dimensional irreducible modules of the universal DAHA of type (C1∨,C1), accepted by Linear and Multilinear Algebra.
- Huang, H.-W. Finite-dimensional modules of the universal Askey–Wilson algebra and DAHA of type (C1∨,C1), submitted.
- Huang, H.-W. (2012). The classification of Leonard triples of QRacah type. Linear Algebra Appl. 436:1442–1472.
- Huang, H.-W. (2015). Finite-dimensional irreducible modules of the universal Askey–Wilson algebra. Commun. Math. Phys. 340:959–984.
- Ito, T., Terwilliger, P. (2010). Double affine Hecke algebras of rank 1 and the Z3-symmetric Askey–Wilson relations. SIGMA. 6(065):9.
- Koornwinder, T. H. (2007). The relationship between Zhedanov’s algebra AW(3) and the double affine Hecke algebra in the rank one case. SIGMA. 3(063):15.
- Koornwinder, T. H. (2008). Zhedanov’s algebra AW(3) and the double affine Hecke algebra in the rank one case. II. The spherical subalgebra. SIGMA. 4(052):17.
- Leonard, D. (1982). Orthogonal polynomials, duality and association schemes. SIAM J. Math. Anal. 13(4):656–663. DOI: 10.1137/0513044.
- Macdonald, I. G. (2003). Affine Hecke Algebras and Orthogonal Polynomials. Cambridge, UK: Cambridge University Press.
- Nomura, K., Terwilliger, P. (2017). The universal DAHA of type (C1∨,C1) and Leonard pairs of q-Racah type. Linear Algebra Appl. 533:14–83.
- Noumi, M., Stokman, J. V. (2004). Askey-Wilson polynomials: an affine Hecke algebraic approach. In: Van Assche, W., Alvarez-Nodarse, R., Marcellan, F., eds. Laredo Lectures on Orthogonal Polynomials and Special Functions. New York, NY: Nova Science Publishers, pp. 111–144.
- Sahi, S. (2000). q-series from a contemporary perspective. Contemp. Math. 254:395–411.
- Sahi, S. (2007). Raising and lowering operators for Askey–Wilson polynomials. SIGMA 3(002):11.
- Terwilliger, P. (2001). Two linear transformations each tridiagonal with respect to an eigenbasis of the other. Linear Algebra Appl. 330(1–3):149–203. DOI: 10.1016/S0024-3795(01)00242-7.
- Terwilliger, P. (2011). The universal Askey–Wilson algebra. SIGMA. 7(069):24.
- Terwilliger, P. (2013). The universal Askey–Wilson algebra and DAHA of type (C1∨,C1). SIGMA. 9(047):40.
- Terwilliger, P., Vidunas, R. (2004). Leonard pairs and the Askey–Wilson relations. J. Algebra Appl. 03(04):411–426. DOI: 10.1142/S0219498804000940.
- Zhedanov, A. (1991). “Hidden symmetry” of Askey–Wilson polynomials, Teoreticheskaya i Matematicheskaya Fizika 89 (1991), 190–204. Theor. Math. Phys. 89(2):1146–1157. DOI: 10.1007/BF01015906.