On bilinear superintegrability for monomial matrix models in pure phase

TL;DR

This paper extends the concept of bilinear superintegrability to monomial matrix models in pure phase, revealing a richer structure with new permutation matrices and N-dependent factors affecting averages.

Contribution

It demonstrates a non-trivial generalization of bilinear superintegrability to monomial matrix models, introducing contour-dependent permutations and complex deformations.

Findings

Bilinear superintegrability applies to monomial matrix models in pure phase.

New permutation matrices depend on contours in the analysis.

Averages involve additional N-dependent factors and complex selection rules.

Abstract

We argue that the recently discovered bilinear superintegrability arXiv:2206.02045 generalizes, in a non-trivial way, to monomial matrix models in pure phase. The structure is much richer: for the trivial core Schur functions required modifications are minor, and the only new ingredient is a certain (contour-dependent) permutation matrix; for non-trivial-core Schur functions, in both bi-linear and tri-linear averages the deformation is more complicated: averages acquire extra N-dependent factors and selection rule is less straightforward to imply.