The Geometric Formula for affine Weyl groups
Access noteAcceso abierto
MetadataShow full item record
Let W be an affine Weyl group with corresponding finite Weyl group Wf . For each λ, a dominant coweight, corresponds an element θ(λ) ∈ W. With N. Libedinsky and D. Plaza, we produce a conjecture called the Geometric Formula predicting the following: the cardinality of the set of elements in W that are lesser or equal to θ(λ) in the Bruhat order, is a linear combination (with coefficients not depending on λ) of the volumes of the faces of the polytope Conv(λ), constructed as the convex hull of the set Wf · λ. We prove the geometric formula for type fA3, by giving general algebraic and geometric constructions for the set ≤ θ(λ). We study the polytope Conv(λ), its faces, and give some formulas to compute their volumes of the corresponding dimension.
Magíster en Ciencias Matemáticas
The following license files are associated with this item: