We establish an isomorphism between the center of the Heisenberg category defined by Khovanov in [13] and the algebra of shifted symmetric functions defined by Okounkov–Olshanski in [18]. We give a graphical description of the shifted power and Schur bases of as elements of , and describe the curl generators of 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]
Revised: 2018-05-11
Accepted: 2018-07-09
Published online: 2019-02-04
DOI: https://doi.org/10.5802/alco.32
Classification: 05E05, 20B30, 18D10
Keywords: Symmetric functions, asymptotic representation theory, Heisenberg categorification, graphical calculus
@article{ALCO_2019__2_1_49_0, author = {Kvinge, Henry and Licata, Anthony M. and Mitchell, Stuart}, title = {Khovanov's Heisenberg category, moments in free probability, and shifted symmetric functions}, journal = {Algebraic Combinatorics}, pages = {49--74}, publisher = {MathOA foundation}, volume = {2}, number = {1}, year = {2019}, doi = {10.5802/alco.32}, zbl = {1405.05188}, mrnumber = {3912168}, language = {en}, url = {alco.centre-mersenne.org/item/ALCO_2019__2_1_49_0/} }
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/item/ALCO_2019__2_1_49_0/
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