Multiplicative Slices, Relativistic Toda and Shifted Quantum Affine Algebras

Michael Finkelberg; Tsymbaliuk A.

doi:10.1007/978-3-030-23531-4_6

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Multiplicative Slices, Relativistic Toda and Shifted Quantum Affine Algebras

Ch. 6. P. 133–304.

Michael Finkelberg, Tsymbaliuk A.

We introduce the shifted quantum affine algebras. They map homomor-
phically into the quantized K-theoretic Coulomb branches of 3d 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 type A open relativistic quantum Toda system.

Keywords: shifted quantum affine algebra relativistic Toda lattice multiplicative slice сдвинутая квантовая аффинная алгебра релятивистская решётка Тоды мультипликативный срез

In book

Representations and Nilpotent Orbits of Lie Algebraic Systems. In Honour of the 75th Birthday of Tony Joseph

Vol. 330. , Switzerland: Birkhauser/Springer, 2019.

Shifted Quantum Affine Algebras: Integral Forms in Type A

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

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 ...

Added: November 14, 2019