Alladi Ramakrishnan Hall

On representations of the rook monoid algebra

Shraddha Srivastava

IMSc

The rook monoid is the monoid of all n by n matrices containing at most one entry equal to 1 in each row and column and zeros elsewhere. In this talk, we will see that the rook monoid algebra is an iterated inflation of symmetric group algebras. We will also explicitly construct the Specht modules of the rook monoid algebra. If time permits,
we will see a Schur-Weyl duality between the rook monoid algebra and the certain subalgebra of the partition algebra.