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Shifted Yangians and shifted quantum affine algebras

Algebra & Discrete Mathematics

Speaker: Oleksandr Tsymbaliuk, Simons Center for Geometry and Physics
Related Webpage: http://www.ic.sunysb.edu/Faculty/otsymbaliuk/
Location: 1147 MSB
Start time: Mon, Nov 28 2016, 4:10PM

In this talk, I will speak about the shifted versions of Yangians and quantum affine algebras as well as their incarnations through geometry of parabolic Laumon spaces, Coulomb branches, additive/multiplicative slices, and Toda lattice.

I will start by reminding the notion of the shifted Yangian (originally introduced by Brundan-Kleshchev in the gl(n) case with a dominant shift and later generalized by Kamnitzer et al to any simple Lie algebra with an arbitrary shift) as well as the recent work relating these algebras to the Coulomb branches.

In the second half, I will discuss the multiplicative analogue of that story. On the algebraic side this leads to the notion of shifted quantum affine algebras, while on the geometric side we replace cohomology by K-theory and affine slices are replaced by multiplicative slices.

This is a joint project with Michael Finkelberg.