Coxeter transformation on cominuscule posets

Emine Yildirim
Friday, September 15, 2017 -
3:30pm to 4:30pm
Vincent Hall 570

Let $P$ be a cominuscule poset which can be thought of as a
parabolic analogue of the poset of positive roots of a finite root
system. Let $J(P)$ be the poset of order ideals of $P$. In this talk,
we will investigate the periodicity of the Coxeter transformation on
the poset $J(P)$, and show that the Coxeter transformation has finite
order for two of the three infinite families of cominuscule posets,
and the exceptional cases. Our motivation comes from a conjecture by
Chapoton which states that the Coxeter transformation has finite order
on the poset $J(R)$ when $R$ is the poset of positive roots of a
finite root system. Our solution is formulated in representation
theory of finite dimensional algebras, and we will further discuss the
results within the same context.