The University of Michigan Combinatorics Seminar


Abstract 

Given a finite Coxeter group W, we define a family of "Cambrian lattices"
associated to W. Each of these lattices is defined as the quotient of the
weak order on W, mod a certain natural congruence. Equivalently, each is
the image of the weak order under a lattice homomorphism. When W is the
symmetric group, the Tamari lattice is one of the Cambrian lattices
associated to W, and when W is B_n, there is a Cambrian lattice which
might be called the type B Tamari lattice. In types A and B, the Cambrian
lattices arise from a(n) (equivariant) fiberpolytope construction,
leading to a fairly complete combinatorial description of these lattices.
Work on the combinatorics in type D is in progress. For W of general
type, one particular Cambrian lattice might be called the "cluster
lattice" due to a close connection to the construction of clusters by
Fomin and Zelevinsky.
The above talk will be preceded by a VIGRE pretalk, also by Nathan Reading,
to be held from 3:153:45pm in 3866 East Hall, i.e. the regular
seminar room. The topic of the pretalk is: 