Grassmannian braiding categorified

Bernhard Keller (Université Paris Diderot - Paris 7, France)

28-May-2020, 12:00-13:00 (4 years ago)

Abstract: Chris Fraser has discovered an action of the extended affine braid group on d strands on the Grassmannian cluster algebra of k-subspaces in n-space, where d is the least common divisor of k and n. We lift this action to the corresponding cluster category first constructed by Geiss-Leclerc-Schröer in 2008. For this, we use Jensen-King-Su's description of this category as a singularity category in the sense of Buchweitz/Orlov. We conjecture an action of the same braid group on the cluster algebra associated with an arbitrary pair of Dynkin diagrams whose Coxeter numbers are k and n. This is a report on ongoing joint work with Chris Fraser.

mathematical physicscommutative algebraalgebraic geometryrings and algebrasrepresentation theorysymplectic geometry

Audience: researchers in the topic

( slides | video )


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