Interlacing adjacent levels of $\beta$-Jacobi corners processes
We study the asymptotic of the global fluctuations for the difference between two
adjacent level in the $\beta$--Jacobi corners process (multilevel and general
$\beta$ extension of the classical Jacobi ensemble of random matrices). The limit
is identified with the derivative of the $2d$ Gaussian Free Field. Our main tool
is integral forms for the (Macdonald-type) difference operators originating from
the Shuffle algebra.