Séminaire Lotharingien de Combinatoire, 78B.63 (2017), 12 pp.

Henry Kvinge, Anthony M. Licata and Stuart Mitchell

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 H' and 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 EndH'(1) 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.

Received: November 14, 2016. Accepted: February 17, 2017. Final version: April 1, 2017.

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