Multiplicative slices, relativistic Toda and shifted quantum affine algebras

Understand

We introduce the shifted quantum affine algebras.

• They map homomorphically into the quantized $K$-theoretic Coulomb branches of $3d\ {\mathcal N}=4$ SUSY quiver gauge theories.
• In type $A$, they are endowed with a coproduct, and they act on the equivariant $K$-theory of parabolic Laumon spaces.
• In type $A_1$, they are closely related to the open relativistic quantum Toda lattice of type $A$.