Alladi Ramakrishnan Hall

$q$-partition algebras

T Geetha

IISER Thiruvananthapuram

Let $V$ be a $n$-dimensional vector space over a field. There are two actions of symmetric group on $V\otimes r$. The symmetric group $S_n$
acts by letter action and the S_r$ acts by place permutations. The action by place permutations can be $q$-deformed to the action of
Iwahori-Hecke algebras and is in Schur-Weyl duality with the natural quantum $GL_n$ action. But there is no obvious $q$-deformed letter action
of $S_n$.

In this talk, we will see a construction of $q$-deformed letter action and $q$-partitions algebras. We also see how this partition algebras
are isomorphic to the $q$-partition algebras defined by Halverson and Thiem. This is a joint work with Richard Dipper.