Séance Séminaire

Séminaire des Doctorant·e·s

Short Story of Residues in Combinatorics

Lie Algebras were introduced at the end of the 19th century and have given birth to a gigantic quantity of beautiful mathematics. One notion which is backed in Lie Algebras is the one of Root Systems. These systems have then been studied for themselves and present great interest for the combinatoritians. To be a bit more precise I will take special interest in type A and specifically in some classes of partitions of a given integer $n$. From there a weird procedure on these partitions gives a link between the root lattice and the affine root lattice which respects the natural action of an important group. This procedure called the Residue will be the hearth of this presentation. Among others these actors will play an important role: - Abaci - Cores - Weyl groups