文献详情
The Higgs and Hahn algebras from a Howe duality perspective
文献类型：期刊
通讯作者：Gaboriaud, J (reprint author), Univ Montreal, Ctr Rech Math, Montreal, PQ, Canada.
期刊名称：PHYSICS LETTERS A影响因子和分区
年：2019
卷：383
期：14
页码：1531-1535
ISSN：0375-9601
关键词：Higgs algebra; Hahn algebra; Howe duality; Commutant; Singular oscillator; Dimensional reduction
所属部门：信息学院
摘要：The Hahn algebra encodes the bispectral properties of the eponymous orthogonal polynomials. In the discrete case, it is isomorphic to the polynomial algebra identified by Higgs as the symmetry algebra of the harmonic oscillator on the 2-sphere. These two algebras are recognized as the commutant of a o(2) circle plus o(2) subalgebra of o(4) in the oscillator representation of the universal algebra U (u(4)). This connection is further related to the embedding of the (discrete) Hahn algebra in U (s ...More
The Hahn algebra encodes the bispectral properties of the eponymous orthogonal polynomials. In the discrete case, it is isomorphic to the polynomial algebra identified by Higgs as the symmetry algebra of the harmonic oscillator on the 2-sphere. These two algebras are recognized as the commutant of a o(2) circle plus o(2) subalgebra of o(4) in the oscillator representation of the universal algebra U (u(4)). This connection is further related to the embedding of the (discrete) Hahn algebra in U (su(1, 1)) circle times U (su(1, 1)) in light of the dual action of the pair (o(4), su(1, 1)) on the state vectors of four harmonic oscillators. The two-dimensional singular oscillator is naturally seen by dimensional reduction to have the Higgs algebra as its symmetry algebra. (C) 2019 Elsevier B.V. All rights reserved. ...Hide

DOI：10.1016/j.physleta.2019.02.024
百度学术：The Higgs and Hahn algebras from a Howe duality perspective
语言：外文
被引频次：1
人气指数：1
浏览次数：1
基金：Natural Science and Engineering Research Council (NSERC) of CanadaNatural Sciences and Engineering Research Council of Canada; NSERCNatural Sciences and Engineering Research Council of Canada; National Foundation of China [11771015]
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