Iwahori-metaplectic duality (Q6560999)

It is considered solvable lattice models and their associated quantum groups appearing in the study of certain Whittaker functions -- special functions from the representation theory of \(p\)-adic algebraic groups. The authors construct a family of solvable lattice models whose partition functions include \(p\)-adic Whittaker functions for general linear groups from two very different sources:from Iwahori-fixed vectors and from metaplectic covers. Interpolating between them by Drinfeld twisting, the authors uncover unexpected relationships between Iwahori and metaplectic Whittaker functions. This leads to new Demazure operator recurrence relations for spherical metaplectic Whittaker functions. In prior work of the authors [\textit{B. Brubaker} et al., Commun. Math. Phys. 380, No. 2, 535--579 (2020; Zbl 1456.82097)] it was shown that the row transfer matrices of certain lattice models for spherical metaplectic Whittaker functions could be represented as `half-vertex operators' operating on the \(q\)-Fock space of Kashiwara, Miwa and Stern. In this paper the same is shown for all constructed lattice models.