2018/08/15 by Julien Gaboriaud, Luc Vinet, Stéphane Vinet +1 · 1 citation
Physics and Astronomy · Mathematics · #math-ph #math.MP #msc:20C35 #msc:22E70 #msc:81R12
paper · pdf · doi:10.1088/1751-8121/aaee1a
9 pages
arxiv created 2018/08/15 · arxiv updated 2018/12/05
The Racah algebra encodes the bispectrality of the eponym polynomials. It is known to be the symmetry algebra of the generic superintegrable model on the 2-sphere. It is further identified as the commutant of the \mathfrako(2) ⊕ \mathfrako(2) ⊕ \mathfrako(2) subalgebra of \mathfrako(6) in oscillator representations of the universal algebra of the latter. How this observation relates to the \mathfraksu(1,1) Racah problem and the superintegrable model on the 2-sphere is discussed on the basis of the Howe duality associated to the pair (\mathfrako(6), \mathfraksu(1,1)).