A \(U(n + 1)\) Bailey lattice (Q2263981)

In this paper it is shown how to transform a \(U(n+1)\) Bailey pair \((A,B)\) relative to \({\mathbf x} = (x_1,x_2,\dots,x_n)\) into a \(U(n+1)\) Bailey pair \((A',B')\) relative to \({\mathbf x}/q = (x_1/q,x_2/q,\dots,x_n/q)\). Combined with Milne's \(U(n+1)\) Bailey lemma, this gives a \(U(n+1)\) Bailey lattice which generalizes the classical Bailey lattice of Agarwal, Andrews, and Bressoud. Tools include the \(U(n+1)\) \(q\)-Chu-Vandermonde and \(U(n+1)\) \(q\)-Pfaff-Saalschütz summations. A number of applications are presented, especially in the case where \((A,B)\) is the unit \(U(n+1)\) Bailey pair.