We classify t-structures and thick subcategories in discrete cluster categories $\mathcal{ C}(\mathcal{ Z})$ of Dynkin type $A$, and show that the set of all t-structures on $\mathcal{ C}(\mathcal{ Z})$ is a lattice under inclusion of aisles, with meet given by their intersection. We show that both the lattice of t-structures on $\mathcal{ C}(\mathcal{ Z})$ obtained in this way and the lattice of thick subcategories of $\mathcal{ C}(\mathcal{ Z})$ are intimately related to the lattice of non-crossing partitions of type $A$. In particular, the lattice of equivalence classes of non-degenerate t-structures on such a category is isomorphic to the lattice of non-crossing partitions of a finite linearly ordered set.
Categories: math.RT math.CT