Multiplicative slices, relativistic Toda and shifted quantum affine algebras

Abstract

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 $A$.

125 pages. v2: references updated; in section 11 the third local Lax matrix is introduced. v3: references updated. v4=v5: 131 pages, minor corrections, table of contents added, Conjecture 10.25 is now replaced by Theorem 10.25 (whose proof is based on the shuffle approach and is presented in a new Appendix). v6: Final version as published, references updated, footnote 4 added

References in corpus (4)

• Coproduct for the Yangian of an affine Kac-Moody algebra
• Shifted quantum affine algebras: integral forms in type $A$ (with appendices by Alexander Tsymbaliuk and Alex Weekes)
• Shifted Yangians and finite W-algebras
• Gelfand-Tsetlin bases for representations of finite W-algebras and shifted Yangians

Cited by in corpus (1)

• Inflations for representations of shifted quantum affine algebras