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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