Parking spaces and Catalan combinatorics for complex reflection groups
Appears in collection : Algebraic Combinatorics in Representation Theory / Combinatoire algébrique en théorie des représentations
Recently, Armstrong, Reiner and Rhoades associated with any (well generated) complex reflection group two parking spaces, and conjectured their isomorphism. This has to be seen as a generalisation of the bijection between non-crossing and non-nesting partitions, both counted by the Catalan numbers. In this talk, I will review the conjecture and discuss a new approach towards its proof, based on the geometry of the discriminant of a complex reflection group. This is an ongoing joint project with Iain Gordon.
