Drinfeld rational fractions for affine Kac-Moody quantum symmetric pairs.

Tomasz Przezdziecki (University of Edinburgh)

Wednesday 20th March 16:00-17:00 Maths 110

Abstract

It is well-known that quantum affine algebras have two distinct presentations, a Kac-Moody presentation and a loop (i.e. new Drinfeld) presentation. It has recently been discovered by Lu and Wang that the same is true for affine KM quantum symmetric pairs, i.e., they admit a loop presentation. This presentation is constructed using a so-called relative braid group action, which is different from the usual Lusztig action. In this talk I will discuss the relation between the loop presentation of a quantum affine algebra and its coideal subalgebra. Of particular interest is the relation between the almost commutative subalgebra used to define Drinfeld polynomials and q-characters (and thus classify finite-dimensional modules) in the quantum affine algebra case, and an analogous subalgebra in the coideal case. I will present several results, including a "factorization theorem" for Cartan-type operators, and a result on approximate compatibility of braid group actions, enabling us to initiate the q-character theory of quantum symmetric pairs. I will also mention potential links with deformed W-algebras. 

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