2013/09/30 by Vincent X. Genest, Luc Vinet, Alexei Zhedanov · 1 citation
Mathematics · Physics and Astronomy · #math-ph #math.MP
paper · pdf · doi:10.1088/1751-8113/47/2/025203
published as J. Phys. A: Math. Theor. 47 (2014) 025203 · 11 pages; Minor changes
arxiv created 2013/11/07 · arxiv updated 2015/06/17
The Racah algebra, a quadratic algebra with two independent generators, is central in the analysis of superintegrable models and encodes the properties of the Racah polynomials. It is the algebraic structure behind the su(1,1) Racah problem as it is realized by the intermediate Casimir operators arising in the addition of three irreducible su(1,1) representations. It has been shown that this Racah algebra can also be obtained from quadratic elements in the enveloping algebra of su(2). The correspondence between these two realizations is here explained and made explicit.