Structure of Grassmannian cluster categories

Abstract: The category of Cohen Macaulay modules over a quotient of a preprojective algebra provides an additive categorification of Scott’s cluster algebra structure of the coordinate ring of the Grassmannian of k-subspaces in n-space, by work of Jensen, King and Su. Under this correspondence, rigid indecomposable objects map to cluster variables. A special role is played by rank 1 indecomposables which correspond bijectively to Plücker coordinates. These are in fact all indecomposables in case k=2. In the other finite types (i.e. $(k,n)\in \{(3,6),(3,7),(3,8)\}$), there are also rank 2 and rank 3 rigid indecomposables. In general, the Grassmannian categories are not well understood. We provide characterisations for these low rank modules in infinite types. This is joint work with Dusko Bogdanic and Ana Garcia Elsener and with Bogdanic, Garcia Elsener and Jianrong Li.

mathematical physicscommutative algebraalgebraic geometryrings and algebrasrepresentation theorysymplectic geometry

Audience: researchers in the topic

( slides | video )

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