REPRESENTATION
THEORY AND RELATED TOPICS SEMINAR
Zajj Daugherty
ABSTRACT: The affine Birman-Murakami-Wenzl (BMW) algebra arises both as an algebra of tangles in a space with one puncture and as the centralizer of orthogonal and symplectic quantum groups on a certain tensor space of modules. The definition of the affine BMW algebra (and its degenerate version) relies on a choice of an infinite family of parameters, though this choice is not free; admissibility conditions have been studied at length. However, when viewing this algebra within the context of its action on tensor space, a family of central elements within the quantum group present themselves as a very natural choice of parameters. These central elements also arise in the study of higher Casimir invariants, and satisfy many beautiful recursion relations. I will outline how these elements arise in the study of centralizer algebras and how they fit into the larger study of both BMW algebras and Lie algebras and quantum groups. (Joint work with Arun Ram and Rahbar Virk.)
For further information visit http://www.northeastern.edu/martsinkovsky/p/rtrt.html or contact Alex Martsinkovsky alexmart >at< neu >dot< edu