{\mathfrak {sl}}_3-Web bases,intermediate crystal bases and categorification |
| |
Authors: | Daniel Tubbenhauer |
| |
Institution: | 1. Centre for Quantum Geometry of Moduli Spaces (QGM), University Aarhus, Aarhus, Denmark
|
| |
Abstract: | We give an explicit graded cellular basis of the \({\mathfrak {sl}}_3\) -web algebra \(K_S\) . In order to do this, we identify Kuperberg’s basis for the \({\mathfrak {sl}}_3\) -web space \(W_S\) with a version of Leclerc–Toffin’s intermediate crystal basis and we identify Brundan, Kleshchev and Wang’s degree of tableaux with the weight of flows on webs and the \(q\) -degree of foams. We use these observations to give a “foamy” version of Hu and Mathas graded cellular basis of the cyclotomic Hecke algebra which turns out to be a graded cellular basis of the \({\mathfrak {sl}}_3\) -web algebra. We restrict ourselves to the \({\mathfrak {sl}}_3\) case over \(\mathbb {C}\) here, but our approach should, up to the combinatorics of \({\mathfrak {sl}}_N\) -webs, work for all \(N>1\) or over \(\mathbb {Z}\) . |
| |
Keywords: | |
本文献已被 SpringerLink 等数据库收录! |
|