Shifted affine iquantum groups of quasi-split ADE types

TL;DR

This paper introduces shifted affine iquantum groups for quasi-split ADE types, providing new algebraic structures and representations that connect to q-deformations of shifted affine Yangians.

Contribution

It formulates shifted affine iquantum groups via Drinfeld presentations and constructs GKLO-type representations using difference operators.

Findings

Constructed GKLO-type representations for shifted affine iquantum groups.

Defined truncated shifted affine iquantum groups.

Established a q-deformation of truncated shifted affine iYangians.

Abstract

We formulate shifted affine iquantum groups of arbitrary quasi-split ADE types via Drinfeld presentations. We construct GKLO-type representations of shifted affine iquantum groups via algebras of difference operators, which allow us to construct truncated shifted affine iquantum groups. This provides a q-deformation of truncated shifted iYangians in our prior work arising as a quantization of affine Grassmannian islices.