The Coxeter Transformation on Cominuscule Posets
Algebras and Representation Theory, vol.22, no.3, pp.699-722, 2019 (SCI-Expanded, Scopus)
- Publication Type: Article / Article
- Volume: 22 Issue: 3
- Publication Date: 2019
- Doi Number: 10.1007/s10468-018-9795-3
- Journal Name: Algebras and Representation Theory
- Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus
- Page Numbers: pp.699-722
- Keywords: Auslander-Reiten translation, Cominuscule posets, Coxeter transformation, Incidence algebras, Representation theory
- Open Archive Collection: AVESIS Open Access Collection
- Galatasaray University Affiliated: Yes
Abstract
Let J(C) be the poset of order ideals of a cominuscule poset C where C comes from two of the three infinite families of cominuscule posets or the exceptional cases. We show that the Auslander-Reiten translation τ on the Grothendieck group of the bounded derived category for the incidence algebra of the poset J(C), which is called the Coxeter transformation in this context, has finite order. Specifically, we show that τ h+ 1 = ±id where h is the Coxeter number for the relevant root system.