Khovanov’s Heisenberg category, moments in free probability, and shifted symmetric functions
Algebraic Combinatorics, Volume 2 (2019) no. 1, pp. 49-74.

We establish an isomorphism between the center End (1) of the Heisenberg category defined by Khovanov in [13] and the algebra Λ * of shifted symmetric functions defined by Okounkov–Olshanski in [18]. We give a graphical description of the shifted power and Schur bases of Λ * as elements of End (1), and describe the curl generators of End (1) in the language of shifted symmetric functions. This latter description makes use of the transition and co-transition measures of Kerov [10] and the noncommutative probability spaces of Biane [2]

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DOI: https://doi.org/10.5802/alco.32
Classification: 05E05,  20B30,  18D10
Keywords: Symmetric functions, asymptotic representation theory, Heisenberg categorification, graphical calculus
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Kvinge, Henry; Licata, Anthony M.; Mitchell, Stuart. Khovanov’s Heisenberg category, moments in free probability, and shifted symmetric functions. Algebraic Combinatorics, Volume 2 (2019) no. 1, pp. 49-74. doi : 10.5802/alco.32. https://alco.centre-mersenne.org/articles/10.5802/alco.32/

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