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.