Alladi Ramakrishnan Hall

Vershik-Okounkov approach to the representation theory of symmetric groups

Ananyo Kazi and Arnab Kundu

We will study complex irreducible representations of S_n. We will define a canonical basis for every irreducible representation of S_n called the GZ-basis. It is known that the GZ-algebra, which acts diagonally on the GZ-basis for every irreducible representation, is generated by the Young-Jucys-Murphy elements. We will define Spec(n) to be the set of all n-tuples obtained by the action of YJM elements on GZ-vectors. Tab(n) will be defined to be the set of all standard Young tableaux on {1, 2, ..., n}. Our final aim will be to show a bijection between Spec(n) and Tab(n) and justify the appearance of Young diagrams and Young tableaux in the theory. Further if time permits we will try to prove that the restriction of an irreducible representation of S_n to S_(n-1) is multiplicity free which will otherwise be assumed throughout the talk.