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BIRS Workshop Lecture Videos

Semistable subcategories and noncrossing tree partitions Garver, Alexander


Semistable subcategories were introduced in the context of Mumford's GIT and interpreted by King in terms of representation theory of finite dimensional algebras. Ingalls and Thomas later showed that for path algebras of Dynkin and extended Dynkin quivers, the poset of semistable subcategories is isomorphic to the corresponding lattice of noncrossing partitions. We classify semistable subcategories for a family of algebras each of which is defined by the choice of a partial triangulation of the disk. Our description also shows that each such semistable subcategory is equivalent to a generalized noncrossing partition. This is joint work with Monica Garcia.

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