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:
Accepted:
Published online:
DOI: 10.5802/alco.32
Keywords: Symmetric functions, asymptotic representation theory, Heisenberg categorification, graphical calculus
Kvinge, Henry 1; Licata, Anthony M. 2; Mitchell, Stuart 2
CC-BY 4.0
@article{ALCO_2019__2_1_49_0,
author = {Kvinge, Henry and Licata, Anthony M. and Mitchell, Stuart},
title = {Khovanov{\textquoteright}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},
mrnumber = {3912168},
zbl = {1405.05188},
language = {en},
url = {https://alco.centre-mersenne.org/articles/10.5802/alco.32/}
}
TY - JOUR AU - Kvinge, Henry AU - Licata, Anthony M. AU - Mitchell, Stuart TI - Khovanov’s Heisenberg category, moments in free probability, and shifted symmetric functions JO - Algebraic Combinatorics PY - 2019 SP - 49 EP - 74 VL - 2 IS - 1 PB - MathOA foundation UR - https://alco.centre-mersenne.org/articles/10.5802/alco.32/ DO - 10.5802/alco.32 LA - en ID - ALCO_2019__2_1_49_0 ER -
%0 Journal Article %A Kvinge, Henry %A Licata, Anthony M. %A Mitchell, Stuart %T Khovanov’s Heisenberg category, moments in free probability, and shifted symmetric functions %J Algebraic Combinatorics %D 2019 %P 49-74 %V 2 %N 1 %I MathOA foundation %U https://alco.centre-mersenne.org/articles/10.5802/alco.32/ %R 10.5802/alco.32 %G en %F 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/articles/10.5802/alco.32/
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