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First formally defined by Borodin and Olshanski, a coherent system on a graded graph is a sequence of probability measures which respect the action of certain down/up transition functions between graded components. In one common example of such a construction, the nth graded component is the set of partitions of n, each measure is the Plancherel measure from the symmetric group, and the down transition function is induced from the restriction functor.

In this talk we will show how to generalize the above framework to towers of Frobenius algebras where we no longer assume semisimplicity. We will explain how the duality between simple and projective modules manifests itself in terms of up and down transition functions in this setting. Finally, we will explain how this all connects to and is motivated by Brundan and Savage's work on Heisenberg categories.