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SUMMARY:The Zamolodchikov relation [Oberseminar Darstellungstheorie]
DTSTART:20260626T121500Z
DTEND:20260626T131500Z
DTSTAMP:20260627T130700Z
UID:indico-event-1424@math-events.uni-bonn.de
DESCRIPTION:Speakers: Liam Rogel (University Kaiserslautern–Landau)\n\nT
 he Hecke algebra is categorified in two ways. Firstly algebraically by Soe
 rgel bimodules\, secondly diagrammatically by the diagrammatic Hecke categ
 ory. The latter category is generated by strands in one color for every ge
 nerating reflection of the underlying Coxeter group\, subject to certain o
 ne-color\, two-color and three-color relations. While in type $A_3$ and $B
 _3$ Elias--Williamson gave an exact description of the three-color (also c
 alled Zamolodchikov) relation\, there is still a gap in type $H_3$. \nEac
 h diagrammatic relation is a certain equality of two morphisms between Bot
 t-Samelsons. We will explain how one can go in-between the algebraic and d
 iagrammatic world to compute how these morphisms factor over all indecompo
 sable summands of these Bott-Samelsons. For this we need to explain the co
 nstruction of idempotents inside the diagrammatic category.\nAs a conseque
 nce we can 1. describe a fake Zamolodchikov relation in $A_3$\, 2. analyse
  all possible variants of Zamolodchikov relations in type $A_3$ and $B_3$\
 , and 3. descibe how one could find the missing gap in $H_3$\, as well as 
 showing how far computer calculations already came.\n\nhttps://math-events
 .uni-bonn.de/event/1424/
LOCATION:MPIM\, Vivatsgasse\,  7 - Seminar Room (Max Planck Institute for 
 Mathematics)
URL:https://math-events.uni-bonn.de/event/1424/
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