Khovanov's Heisenberg category, moments in free probability, and shifted symmetric functions

Abstract

We establish an isomorphism between the center EndH'(1) of Khovanov's Heisenberg category H1, the algebra λ° of shifted symmetric functions defined by Okounkov-Olshanski. We give a graphical description of the shifted power and Schur bases of λ∗as elements of EndH'(1), and describe the curl generators of EndH1p1q in the language of shifted symmetric functions. This latter description makes use of the transition and co-transition measures of Kerov and the noncommutative probability spaces of Biane. Show more