Racah algebras, the centralizer \(Z_n(\mathfrak{sl}_2)\) and its Hilbert-Poincaré series (Q2145160)

The paper under review shows that a certain quotient \(sR(n)\) of the higher rank Racah algebra \(R(n)\) by a centrally generated ideal is isomorphic to the centralizer of the diagonal embedding of \(U(\mathfrak{sl}_2)\) into \(U(\mathfrak{sl}_2)^{\otimes n}\). This description is used to give a presentation of \(sR(n)\) and to determine the Hilbert-Poincaré series of this algebra. Some extensions and generalizations of these results are discussed.