Annales Henri Poincaré ( IF 1.4 ) Pub Date : 2020-10-21 , DOI: 10.1007/s00023-020-00972-8 Nicolas Crampé , Wouter van de Vijver , Luc Vinet
The oscillator Racah algebra \(\mathcal {R}_n(\mathfrak {h})\) is realized by the intermediate Casimir operators arising in the multifold tensor product of the oscillator algebra \(\mathfrak {h}\). An embedding of the Lie algebra \(\mathfrak {sl}_{n-1}\) into \(\mathcal {R}_n(\mathfrak {h})\) is presented. It relates the representation theory of the two algebras. We establish the connection between recoupling coefficients for \(\mathfrak {h}\) and matrix elements of \(\mathfrak {sl}_n\)-representations which are both expressed in terms of multivariate Krawtchouk polynomials of Griffiths type.
中文翻译:
振荡器代数,李代数$$ \ mathfrak {sl} _n $$ sl n的Racah问题,以及多元Krawtchouk多项式
振荡器Racah代数\(\ mathcal {R} _n(\ mathfrak {h})\)由中间Casimir算子实现,该中间Casimir算子出现在振荡器代数\(\ mathfrak {h} \)的张量积中。提出了李代数\(\ mathfrak {sl} _ {n-1} \)到\(\ mathcal {R} _n(\ mathfrak {h})\)的嵌入。它涉及两个代数的表示理论。我们建立\(\ mathfrak {h} \)的重新耦合系数与\(\ mathfrak {sl} _n \) -表示的矩阵元素之间的联系,它们均用格里菲思类型的多元Krawtchouk多项式表示。