The Letzter map for quantum symmetric pairsOberseminar Darstellungstheorie

by Stefan Kolb (Newcastle)

Friday Jun 27, 2025, 2:15 PM → 3:15 PM Europe/Berlin

Endenicher Allee 60/1.008- Seminarraum (Mathezentrum)

A crucial ingredient in the theory of quantum symmetric pairs (QSP) is the quasi K-matrix which is an analogue of the quasi R-matrix in the theory of quantum groups. The quasi K-matrix plays an important role in the construction of canonical bases, universal K-matrices and braid group actions for quantum symmetric pairs. The quasi K-matrix is constructed by an intricate induction argument. 

In this talk, I will explain how the quasi K-matrix can be directly obtained from the quasi R-matrix via a projection map first considered by G. Letzter. This was first observed in the quasi-split case in joint work with M. Yakimov, but turns out to hold in full generality. The Letzter map can also be used to obtain presentations of QSP-algebras in terms of generators and relations.