İstanbul Technical University Mathematical Engineering Department Seminars

The Coxeter Transformation on Grid Posets
Emine Yıldırım
Özet : Let $P_{k,n}$ be a grid poset, i.e., the product of two chains, of length $k$ and $n$. Let $J(P_{k,n})$ be the poset of order ideals of $P_{k,n}$, and $A$ be the incidence algebra of the poset $J(P_{k,n})$. In this talk, we will first give the definition of Coxeter transformation $\tau$ , and then investigate periodicity of $\tau$ for the algebra $A$. It is a well-known result that $\tau$ is periodic for hereditary algebras. This result extended to piecewise hereditary algebras by $S$. Ladkani. The algebra A we will investigate in this talk is neither hereditary nor piecewise hereditary, but we will show that $\tau$ is periodic in this case too. Our result extends further to two of the three infinite families of cominuscule posets.