Drinfeld rational functions for quantum affine symmetric pairs

by Tomasz Przeździecki (University of Edinburgh)

Friday Jan 17, 2025, 2:15 PM → 3:15 PM Europe/Berlin

Endenicher Allee 60, 1.008- Seminarraum (Mathezentrum)

It is well known that quantum affine algebras admit three distinct presentations (Kac-Moody, new Drinfeld and RTT). Relatively recently, the same has been shown to hold for a broad family of quantum affine symmetric pairs. In particular, a Drinfeld-type presentation, due to Lu-Wang, is a new and exciting development.

 

The focus of my talk will be the relationship between the usual Drinfeld presentation of quantum affine algebras and the Lu-Wang presentation of their coideal subalgebras. Remarkably, both presentations exhibit large commutative subalgebras, which are of particular interest to representation theory. More specifically, I will present several results concerning the properties of the generators of these commutative subalgebras, including their behaviour under inclusion and the coproduct, as well as their spectra on finite-dimensional representations. I will also discuss applications to the nascent theory of q-characters of quantum symmetric pairs.