On the N=2 superconformal index and eigenfunctions of the elliptic RS model

Abstract: We define an infinite sequence of superconformal indices, I_n, generalizing the Schur index for N=2 theories. For theories of class S we then suggest a recursive technique to completely determine I_n. The information encoded in the sequence of indices is equivalent to the N=2 superconformal index depending on the maximal set of fugacities. Mathematically, the procedure suggested in this note provides a perturbative algorithm for computing a set of eigenfunctions of the elliptic Ruijsenaars-Schneider model.