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.