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تسجيل مستخدم جديدThe Racah algebra as a commutant and Howe duality
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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 $mathfrak{o}(2) oplus mathfrak{o}(2) oplus mathfrak{o}(2)$ subalgebra of $mathfrak{o}(6)$ in oscillator representations of the universal algebra of the latter. How this observation relates to the $mathfrak{su}(1,1)$ Racah problem and the superintegrable model on the $2$-sphere is discussed on the basis of the Howe duality associated to the pair $big(mathfrak{o}(6)$, $mathfrak{su}(1,1)big)$.
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