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The Coxeter Transformation on Cominuscule Posets

Authors
  • Yildirim, Emine
Type
Published Article
Journal
Algebras and Representation Theory
Publisher
Springer Netherlands
Publication Date
May 04, 2018
Volume
22
Issue
3
Pages
699–722
Identifiers
DOI: 10.1007/s10468-018-9795-3
Source
Springer Nature
Keywords
License
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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 τh+ 1 = ±id where h is the Coxeter number for the relevant root system.

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