Department of Mathematics and Statistics

Department of Mathematics and Statistics
Department of Mathematics and Statistics

Geometry and Representation Theory Seminar


Monday, September 24th, 2018

Time: 4:30-5:30 p.m.  Place: Jeffery Hall 319

Speaker: Emine Yildrim (Queen's University)

Title: The bounded derived category for cominuscule posets

Abstract:  Cominuscule posets come from root posets and have connections to Lie theory and Schubert calculus. We are interested in whether the bounded derived category of the incidence algebra of a cominuscule poset is fractionally Calabi-Yau. In other words, we ask if some non-zero power of the Serre functor is a shift functor. We answer this question on the level of the Grothendieck groups. On the Grothendieck group this functor becomes an endomorphism called the Coxeter transformation. We show that Coxeter transformation has finite order for two of the three infinite families of cominuscule posets, and for the exceptional cases. Our motivation comes from a conjecture by Chapoton which states that the bounded derived category of incidence algebra of root posets is fractionally Calabi-Yau. Our result can be thought of as a parabolic analogue of Chapoton's conjecture.