  We propose quantum Hamiltonians of the double elliptic many-body integrable
system (DELL) and study its spectrum. These Hamiltonians are certain elliptic
functions of coordinates and momenta. Our results provide quantization of the
classical DELL system which was previously found in the string theory
literature. The eigenfunctions for the N-body model are instanton partition
functions of 6d SU(N) gauge theory with adjoint matter compactified on a torus
with a codimension two defect. As a byproduct we discover new family of
symmetric orthogonal polynomials which provide an elliptic generalization to
Macdonald polynomials.
