The Coxeter Transformation on Cominuscule Posets
Algebras and Representation Theory, cilt.22, sa.3, ss.699-722, 2019 (SCI-Expanded, Scopus)
- Yayın Türü: Makale / Tam Makale
- Cilt numarası: 22 Sayı: 3
- Basım Tarihi: 2019
- Doi Numarası: 10.1007/s10468-018-9795-3
- Dergi Adı: Algebras and Representation Theory
- Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus
- Sayfa Sayıları: ss.699-722
- Anahtar Kelimeler: Auslander-Reiten translation, Cominuscule posets, Coxeter transformation, Incidence algebras, Representation theory
- Açık Arşiv Koleksiyonu: AVESİS Açık Erişim Koleksiyonu
- Galatasaray Üniversitesi Adresli: Evet
Özet
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.