• A
• A
• A
• ABC
• ABC
• ABC
• А
• А
• А
• А
• А
Regular version of the site

## Shifted Quantum Affine Algebras: Integral Forms in Type A

Arnold Mathematical Journal. 2019. Vol. 5. No. 2-3. P. 197-283.
Michael Finkelberg, Tsymbaliuk A.

We define an integral form of shifted quantum affine algebras of type A and construct
Poincaré–Birkhoff–Witt–Drinfeld bases for them. When the shift is trivial, our integral
form coincides with the RTT integral form. We prove that these integral forms are
closed with respect to the coproduct and shift homomorphisms. We prove that the
homomorphism from our integral form to the corresponding quantized K -theoretic
Coulomb branch of a quiver gauge theory is always surjective. In one particular case
we identify this Coulomb branch with the extended quantum universal enveloping
algebra of type A. Finally, we obtain the rational (homological) analogues of the
above results [proved earlier in Kamnitzer et al. (Proc Am Math Soc 146(2):861–874,
2018a; On category O for affine Grassmannian slices and categorified tensor products.
arXiv:1806.07519, 2018b) via different techniques].