Heaps, Crystals and Preprojective algebra modules

Abstract: Kashiwara crystals are combinatorial gadgets associated to a representation of a reductive algebraic group that enable us to understand the structure of the representation in purely combinatorial terms. We will describe a type-independent construction of crystals of certain representations, using the heap associated to a fully commutative element in the Weyl group. Then we will discuss how these heaps also lead us to the construction of modules for the preprojective algebra of the Dynkin quiver. Using the rank-nullity theorem, we will see how the Kashiwara operators have a surprisingly nice description in terms of these preprojective algebra modules. This is work in progress joint with Anne Dranowski, Joel Kamnitzer, Tanny Libman and Calder Morton-Ferguson.

mathematical physicsalgebraic geometrydifferential geometrygeometric topologyoperator algebrasrepresentation theorysymplectic geometry

Audience: researchers in the topic

Geometry, Physics, and Representation Theory Seminar

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