Integer partitions and characters of Lie algebras (Jehanne Dousse, Université Lyon I))

15.03.2022 10:30

A partition of a positive integer n is a non-increasing sequence of positive integers whose sum is n. In the 1980's, Lepowsky and Wilson established a connection between the Rogers-Ramanujan partition identities and the representation theory of the affine Lie algebra A_1^{(1)}. Other representation theorists have then extended their method and discovered new identities yet unknown to combinatorialists.
After presenting the history of the interactions between the two fields, we will introduce a new generalisation of partitions which is better suited to make the connection with representation theory, and show how it can be used to prove refined partition identities and non-specialised character formulas.
This is joint work with Isaac Konan.

Lieu

Bâtiment: Conseil Général 7-9

Room 1-05,Tuesday 15.03.2022, Séminaire "Groupes et géométrie"

entrée libre