**Ben Tharp**

**The Marked Brauer Algebra**

It is well known that, on a certain tensor space, the actions of the

symmetric group and the general linear group commute. In 1937, Richard

Brauer defined an algebra which replaces the role of the symmetric group

when the general linear group is replaced by the orthogonal group,

symplectic group, or the orthosymplectic Lie superalgebra. More recently,

Dongho Moon described an algebra whose action commutes with the action of

the Lie superalgebra of Type P. But while Brauer's algebra has an easy

description using certain "Brauer diagrams," Moon's algebra is given by

generators and relations. In recent work with Jon Kujawa, we give a

diagrammatic description of Moon's algebra which generalizes the Brauer

algebra in a natural way.