Tensor products, q-characters and R-matrices for quantum toroidal algebras

by Duncan Laurie (University of Edinburgh,)

Friday May 9, 2025, 2:15 PM → 3:15 PM Europe/Berlin

Endenicher Allee 60/Room 1.008 (Mathezentrum)

Quantum toroidal algebras are the ‘double affine’ objects within the quantum setting. In particular, they contain – and are generated by – horizontal and vertical quantum affine subalgebras.

 

These quantum toroidal algebras are not known to possess a coproduct, but do have a topological coproduct mapping to a completion of the tensor square. However, this still fails to produce a tensor product on the category of integrable modules due to the presence of infinite sums.

 

In this talk, after introducing the quantum toroidal algebras, I shall explain how to overcome these issues – namely, we'll obtain well-defined tensor products satisfying various nice properties. (For example, there are compatibilities with both Drinfeld polynomials and q-characters, as well as toroidal R-matrices that solve the Yang-Baxter equation.)