Italian Representation Theory Seminar

Oleksandr Tsymbaliuk, Purdue University

Shifted Yangians and quantum affine algebras revisited

Organizer's time: 2021-06-25 15:00 Europe/Rome

Duration: 1 hour

Access information: The seminar will be held on Microsoft Teams.

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In the first part of the talk, I will recall some basic results about shifted Yangians (and their trigonometric versions-the shifted quantum affine algebras), which first appeared in the work of Brundan-Kleshchev relating type A Yangians and finite W-algebras and have become a subject of renewed interest over the last 5 years due to their close relation to quantized Coulomb branches introduced by Braverman-Finkelberg-Nakajima.

In the second part of the talk, I will try to convince that the case of antidominant shifts (opposite to what was originally studied in the work of Brundan-Kleshchev in type A and of Kamnitzer-Webster-Weekes-Yacobi in general type) is of particular importance as the corresponding algebras admit the RTT realization (at least in the classical types). In particular, this provides a conceptual explanation of the coproduct homomorphisms, gives rise to the integral forms of shifted quantum affine algebras, and also yields a family of (conjecturally) integrable systems on the corresponding Coulomb branches. As another application, the GKLO-type homomorphisms used to define truncated version of the above algebras provide a wide class of rational/trigonometric Lax matrices in classical types.

This talk is based on the joint works with Michael Finkelberg as well as Rouven Frassek and Vasily Pestun.

Submitted by: Andrea Appel