Peter Koroteev, UC Berkeley – Physically Inspired Mathematics Seminar

Title: The Quantum DELL System

Abstract: 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 eigenfunction for the N-body model is conjectured to be a properly normalized equivariant elliptic genus of the affine Laumon space (in physics terms — an 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.