文献详情
HEUN ALGEBRAS OF LIE TYPE
文献类型：期刊
通讯作者：Crampe, N (reprint author), Univ Orleans, Inst Denis Poisson, Univ Tours, CNRS,UMR 7013, Parc Grammt, F-37200 Tours, France.; Crampe, N (reprint author), Univ Montreal, Ctr Rech, Math, Ctr Ville Stn, POB 6128, Montreal, PQ H3C 3J7, Canada.
期刊名称：PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY影响因子和分区
年：2020
卷：148
期：3
页码：1079-1094
ISSN：0002-9939
摘要：We introduce Heun algebras of Lie type. They are obtained from bispectral pairs associated to simple or solvable Lie algebras of dimension three or four. For su(2), this leads to the Heun-Krawtchouk algebra. The corresponding Heun-Krawtchouk operator is identified as the Hamiltonian of the quantum analogue of the Zhukovsky-Voltera gyrostat. For su(1, 1), one obtains the Heun algebras attached to the Meixner, Meixner-Pollaczek, and Laguerre polynomials. These Heun algebras are shown to be isomorp ...More
We introduce Heun algebras of Lie type. They are obtained from bispectral pairs associated to simple or solvable Lie algebras of dimension three or four. For su(2), this leads to the Heun-Krawtchouk algebra. The corresponding Heun-Krawtchouk operator is identified as the Hamiltonian of the quantum analogue of the Zhukovsky-Voltera gyrostat. For su(1, 1), one obtains the Heun algebras attached to the Meixner, Meixner-Pollaczek, and Laguerre polynomials. These Heun algebras are shown to be isomorphic to the the Hahn algebra. Focusing on the harmonic oscillator algebra ho leads to the Heun-Charlier algebra. The connections to orthogonal polynomials are achieved through realizations of the underlying Lie algebras in terms of difference and differential operators. In the su(1, 1) cases, it is observed that the Heun operator can be transformed into the Hahn, Continuous Hahn, and Confluent Heun operators, respectively. ...Hide

DOI：10.1090/proc/14788
百度学术：HEUN ALGEBRAS OF LIE TYPE
语言：外文
基金：Natural Science and Engineering Council (NSERC) of CanadaNatural Sciences and Engineering Research Council of Canada; National Science Foundation of ChinaNational Natural Science Foundation of China [11711015]
作者其他论文



The Racah algebra as a commutant and Howe duality.Gaboriaud, Julien, Vinet, Luc, Vinet, Stephane, et al. .JOURNAL OF PHYSICS A-MATHEMATICAL AND THEORETICAL. 2018, 51(50).
Algebraic Heun Operator and Band-Time Limiting.Grunbaum, F. Alberto, Vinet, Luc, Zhedanov, Alexei,.COMMUNICATIONS IN MATHEMATICAL PHYSICS. 2018, 364(3), 1041-1068.
The dual pair Pin (2n) x osp(1 vertical bar 2), the Dirac equation and the Bannai-Ito algebra.Gaboriaud, Julien, Vinet, Luc, Vinet, Stephane, et al. .NUCLEAR PHYSICS B. 2018, 937, 226-239.
The Higgs and Hahn algebras from a Howe duality perspective.Frappat, Luc, Gaboriaud, Julien, Vinet, Luc, et al. .PHYSICS LETTERS A. 2019, 383(14), 1531-1535.
Perfect state transfer in a spin chain without mirror symmetry.Coutinho, Gabriel, Vinet, Luc, Zhan, Hanmeng, et al. .JOURNAL OF PHYSICS A-MATHEMATICAL AND THEORETICAL. 2019, 52(45).