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BIRS Workshop Lecture Videos

The orbits of the Coxeter Transformation and Rowmotion for cominuscule posets Yıldırım, Emine


Let h to be the Coxeter number of a root system. We show that the Coxeter transformation of the incidence algebra coming from the order ideals in a cominuscule poset is periodic of order 'h+1' (up to a sign) in most cases using tools from representation theory of algebras. On the other hand, there is a combinatorial action, called the Rowmotion, defined on cominuscule posets. It is well-known that this action has order 'h' on the order ideals of a cominuscule poset. In this talk, we will demonstrate combinatorial similarities of the orbits of these two actions.

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