A non-Levi branching rule in terms of Littelmann paths

Date/heure
26 septembre 2016
15:30 - 16:30

Oratrice ou orateur
Jacinta Torres

Catégorie d'évènement
Séminaire de géométrie complexe

Résumé

The Littelmann paths model is a strong tool used to understand finite-dimensional representations of complex semi-simple Lie algebras. It has remarkable applications, such as a rule for the the decomposition into simple summands of the tensor product of two irreducible representations and of the restriction of a simple representation to a Levi sub algebra (those obtained by removing nodes from the Dynkin diagram). Such rules are called branching rules. We prove a conjecture of Naito-Sagaki about a branching rule for the restriction of irreducible representations of $m a t h f r a k s l (2 n, m a t h b b C)$ to $m a t h f r a k s p (2 n, m a t h b b C)$ in terms of Littelmann paths. The embedding is given by the folding of the type $A_{2 n - 1}$ Dynkin diagram, and is not of Levi type. So far, no non-Levi branching rules were known in terms of Littelmann paths. This is joint work with Bea Schumann.