REPRESENTATION
THEORY AND RELATED TOPICS SEMINAR
ABSTRACT: We
use the language of higher category theory to define what we call a
"symmetric self-adjoint Hopf" (SSH) structure on a semisimple abelian
category. SSH categories are the categorical analog of positive
self-adjoint Hopf algebras studied by A.Zelevinsky. It follows from his
work that for every positive self-adjoint Hopf algebra the Heisenberg
double is equipped with a natural action on the algebra. We obtain
categorical analogs of the Heisenberg double and its action from the
SSH structure on a category in a canonical way. We exhibit the SSH
structure on the category of polynomial functors. The categorical
Heisenberg double in this case provides a categorification of the
infinite dimensional Heisenberg algebra related to the categorification
proposed by M. Khovanov.
The preprint is available on arXiv:1406.3973.
For further information visit http://www.northeastern.edu/martsinkovsky/p/rtrt.html or contact Alex Martsinkovsky alexmart >at< neu >dot< edu