Fonctionne avec Indico
v3.2.9
A large area of study in algebra and topology is that of Lie groups, and their linear counterparts the Lie algebras. The product in Lie algebras being slightly unusual, these objects are better understood by another linearization process: representation theory. The representation theory of Lie algebras is entirely encoded in an associative monoid called the plactic monoid. This monoid admits two notable different characterizations: by a presentation via generators and relations, and as a crystal monoid. In this talk I will discuss how these two approaches interact with one another, a byproduct of which are certain infinite dimensional extensions of these monoids. The components of these infinite dimensional extensions can be parametrized by a graphical calculus called trees. These construction open up an approach towards studying homological and homotopical properties of the plactic monoids.