$Q$-functions for lambda opers

Abstract

We consider the Schrödinger operators which are constructed from the $\hat{I}»$-opers corresponding to solutions of the ${\widehat{\mathfrak{sl}}}_2$ Gaudin Bethe Ansatz equations. We define and study the connection coefficients called the $Q$-functions. We conjecture that the $Q$-functions obtained from the $\hat{I}»$-opers coincide with the $Q$-functions of the Bazhanov-Lukyanov-Zamolodchikov opers with the monster potential related to the quantum KdV flows. We give supporting evidence for this conjecture.

Revised version, new section about the action of the reproduction procedures on opers and Q functions. 1 figure