中央研究院數學研究所

Seminar in Representation Theory

Computing in the asymptotic category

2026/03/10 (Tue.) 16:30~17:30

Date : 2026/03/10 (Tue.) 16:30~17:30
Location : Seminar Room 617, Institute of Mathematics (NTU Campus)
Speaker : Liam Rogel (University of Kaiserslautern–Landau)
Abstract :
The diagrammatic Hecke category, introduced by Elias--Williamson, provides a graphical way of studying the category of Soergel bimodules. In recent joint work with Ben Elias and Dani Tubbenhauer we gave an algorithm to compute idempotents in this category. We present this, and show how one can compute dimensions of objects in the asymptotic Hecke category. Furthermore we give a preview of computer calculations that will appear in a forthcoming sequel, obtained by extending the Magma package ASLoc. This implementation automates much of the recursive computation, making it possible to effectively compute idempotents and the corresponding dimensions in concrete examples.