Shifted Quantum Affine Algebras: Integral Forms in Type A

Michael Finkelberg, Alexander Tsymbaliuk

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10 Citations (Scopus)


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].

Original languageEnglish
Pages (from-to)197-283
Number of pages87
JournalArnold Mathematical Journal
Issue number2-3
Publication statusPublished - 1 Nov 2019


  • Coulomb branch
  • Drinfeld-Gavarini duality
  • Evaluation homomorphism
  • PBWD bases
  • Shifted quantum affine algebras
  • Shifted Yangians


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