A quantization of the harmonic analysis on the infinite-dimensional unitary group
The paper under review studies a non-trivial \(q\)-discretization of certain problems related to the harmonic analysis on the infinite dimensional unitary group \(U(\infty)\). The study leads to a new family of determinantal point processes which are connected to pseudo big \(q\)-Jacobi polynomials. These new point processes live on a double \(q\)-lattice and it is shown that their correlation kernels can be expressed through the basic hypergeometric function \({}_2\phi_1\). The main tool introduced in the paper is an extended version of the Gelfand-Tsetlin graph. The \(q\)-boundary of the latter is determined.
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