### Arun Ram

University of Wisconsin

### q-analogues of diagram algebras

**Friday 27th September, 12-1pm,
Carslaw 373. **
The group algebras of the symmetric groups
are contained in the Brauer algebras and
these in turn contain the Temperley Lieb algebras
and are contained in the partition algebras (discovered
by V. Jones). All the other centralizer algebras of
this type (diagram algebras) are contained in the
partition algebras (invented by V. Jones).

A q-analogue of the group algebra of the symmetric group
is given by the Iwahori-Hecke algebras of type A,
and the BMW algebras are the right q-analogue of
the Brauer algebras. It has been open for some
time how to build a good q-analogue of the partition
algebras. In this talk I will explain how we
settle this question. This is joint work with T. Halverson.