Elliptic triad

Abstract

The triad refers to embedding the Macdonald polynomials into the Noumi-Shiraishi functions and their reduction to solutions of simple linear equations at particular values of t. It provides an alternative definition of Macdonald theory. We discuss lifting the triad to an elliptic generalization of the Noumi-Shiraishi functions. The central unknown ingredient is linear equations, for which we discuss various possible approaches, including immediate elliptic deformation of periodicity conditions, (elliptic) Ding-Iohara-Miki algebra operators, and elliptic Kostka coefficients.