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

  • Author(s): Kvinge, Henry
  • Licata, Anthony M.
  • Mitchell, Stuart
  • et al.

Published Web Location

https://arxiv.org/pdf/1610.04571.pdf
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Abstract

We establish an isomorphism between the center of the Heisenberg category defined by Khovanov and the algebra $\Lambda^*$ of shifted symmetric functions defined by Okounkov-Olshanski. We give a graphical description of the shifted power and Schur bases of $\Lambda^*$ as elements of the center, and describe the curl generators of the center 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.

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