Research Seminar 7
Date/Time: 16.09.2021, 11:00 am.
Partition Algebras and their representation theory
Sadhanand Vishwanath
Chennai Mathematical Institute.
16-09-21

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Abstract

For a natural number n, the partition algebra A_n is related to the symmetric group via a Schur-Weyl Duality. In the tower of partition algebras A_1 \subset A_2 \subset ... , we have idempotents e_n \in A_n such that e_n A_n e_n = A_(n-1).

In general, if e is an idempotent in a finite dimensional algebra A, then eAe is an algebra with e as its identity. The category of eAe-modules embeds in to the category of A-modules. This allows us to construct some of the simple A modules from simple eAe-modules and the remaining simple A-modules L are characterised by eL=0.

This situation at each level of the partition algebra tower allows us to recursively analyse the representation theory of the entire tower.

In this talk, I will define Partition algebras and discuss their representation theory.