Towards elliptic deformation of $q,t$-matrix models

Abstract: As a necessary step in constructing elliptic matrix models, which preserve the superintegrability property $<char>\sim {\rm char}$, we suggest an elliptic deformation of the peculiar loci $p_k^{\Delta_n}$, which play an important role in precise formulation of this property. The suggestion is to define the $p_k^{\Delta_n}$-loci as elliptic functions with the right asymptotics at $\tau\to i\infty$. If this hypothesis is correct, one can move to substituting the Schur and Macdonald functions in the role of characters by the elliptic GNS and study their behavior at the deformed topological and $\Delta$ loci.