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Presented By: Learning Seminar in Algebraic Combinatorics - Department of Mathematics

Learning seminar in algebraic combinatorics: Weak order and Cambrian Lattices

Paul Mammen

In this talk we will look at another important example of semi distributive lattices, the weak order on finite Coxeter groups. In the specific example of the symmetric group, which can be associated to the type A Dynkin quiver, we will see how the familiar lattice of torsion classes can be identified with a quotient of the weak order. Building on this example, we will generalize the quotient construction to finite Coxeter groups via the notion of Cambrian congruences and Cambrian lattices.

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