Categorification of infinite Grassmannians

Abstract: Jensen, King, and Su introduce the Grassmannian cluster categories. In the talk, we will discuss the analogous of their construction to the Grassmannian of infinite rank. We show that there is a structure preserving bijection between the generically free rank one modules in a Grassmannian category of infinite rank and the Plücker coordinates in a Grassmannian cluster algebra of infinite rank. We developed a new combinatorial tool to determine when two k-subsets of integers are `non-crossing’, i.e., when two Plücker coordinates of the Grassmannian cluster algebras of infinite rank are compatible. This is a joint work with Jenny August, Eleonore Faber, Sira Gratz, and Sibylle Schroll.

commutative algebraalgebraic geometrycombinatoricsrings and algebrasrepresentation theory

Audience: researchers in the topic

Geometry, Algebra, Singularities, and Combinatorics

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