Digjoy Paul

Tata Institute of Fundamental Research, Mumbai

June 15

Joint work with Sridhar Narayanan (IMSc Chennai)and Shraddha Srivastava (Uppsala University)

ALCoVE 2021

A multiset generalization of (set) partition algebra

(based on arXiv:1903.10809)

1. Classical Scur--Weyl duality

3.Multiset partition algebra

2.Partition algebra

4. Cellularity and semi-simplicity

5.Multiset tableaux,Plethysm andRestriction problem

Plan for the talk

Schur--Weyl duality

Diagram Algebras

Partition Algebras

Natural Questions

What plays the role of Partition Algebras?

A new diagram algebra based on multiset partitions

Multiplication of two bipartitite multi graphs

Orbit basis of Partition algebras

A new Schur--Weyl duality

Combinatorial Representation theory

(Orellana-Zabrocki)

Multiset Tableaux

# semistandard Multiset tableauxof shape

Colmenarejo, Orellana, Saliola, Schlling, Zabrocki

(N,P,S)

Multiset tableaux--Plethysm--Restriction problem

Thm:(N,P,S)

Schur

Thank you for your attention!